Function Notation: CCSS.Math.Content.HSF-IF.A.2 - Common Core: High School - Functions

Card 0 of 48

Question

Given the following function , calculate .

$f(x)=\frac{1}{x}+\sqrt{3x-5}$

Assume is always positive.

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.Math.content.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is three.

$f(3)\rightarrow x=3$

Step 2: Given the function, input the desired value.

In step one the input value of three was found. Now substitute 3 in for every in the function.

$\f(x)=\frac{1}{x}+\sqrt{3x-5} \ \f(3)=\frac{1}{3}+\sqrt{3(3)-5} \ \ f(3)=\frac{1}{3}+\sqrt{9-5} \ \f(3)=\frac{1}{3}+\sqrt{4} \ \f(3)=\frac{1}{3}+ 2 \ \f(3)=\frac{7}{3}$

Step 3: Answer the question.

The answer is

$f(3)=\frac{7}{3}$

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Question

Given the following function , calculate .

$g(x)=\frac{x^2-3}{x^3+1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is two.

$g(2)\rightarrow x=2$

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function.

$g(x)=\frac{x^2-3}{x^3+1}$

$g(2)=\frac{2^2-3}{2^3+1}$

$g(2)=\frac{2^2-3}{2^3+1}$

$g(2)=\frac{4-3}{8+1}$

$g(2)=\frac{1}{9}$

Step 3: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

$g(2)=\frac{1}{9}$

Compare your answer with the correct one above

Question

Given the following functions and , calculate .

$\f(x)=3x+2 \g(x)=x^2-2x+1$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form and the question asks to calculate we know that the input value is two.

$f(2)\rightarrow x=2$

After the function value of is calculated, it will be the input value for .

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function .

$\ f(2)=3(2)+2 \f(2)=6+2 \f(2)=8$

Step 3: Substitute the function value of the inside portion into .

$\g(x)=x^2-2x+1 \g(8)=8^2-2(8)+1 \g(8)=64-16+1 \g(8)=49$

Compare your answer with the correct one above

Question

Given the following function , calculate .

$f(x)=\frac{x^2-10}{x}+2x$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is five.

$f(5)\rightarrow x=5$

Step 2: Given the function, input the desired value.

In step one the input value of five was found. Now substitute 5 in for every in the function.

$f(x)=\frac{x^2-10}{x}+2x$

$f(5)=\frac{5^2-10}{5}+2(5)$

$f(5)=\frac{25-10}{5}+10$

$f(5)=\frac{15}{5}+10$

Step 3: Verify solution by graphing function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(5)=13$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Calculate for the function .

$f(x)=x-\frac{1}{2x+3}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is negative three.

$f(-3)\rightarrow x=-3$

Step 2: Given the function, input the desired value.

In step one the input value of negative three was found. Now substitute negative three in for every in the function.

$f(x)=x-\frac{1}{2x+3}$

$f(-3)=-3-\frac{1}{2(-3)+3}$

$f(-3)=-3-\frac{1}{-6+3}$

$f(-3)=-3-\frac{1}{-3}$

$f(-3)=\frac{9}{-3}-\frac{1}{-3}$

$f(-3)=\frac{9-1}{-3}$

$f(-3)=-\frac{8}{3}$

Step 3: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

$f(-3)=-\frac{8}{3}$ .

Compare your answer with the correct one above

Question

Calculate .

$f(x)=3x-\frac{x^2}{x-1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form and the question asks to calculate we know that the input value is negative two.

$f(-2)\rightarrow x=-2$

After the function value of is calculated, it will be the input value for .

Step 2: Given the function, input the desired value.

In step one the input value of negative two was found. Now substitute -2 in for every in the function .

$f(x)=3x-\frac{x^2}{x-1}$

$f(-2)=3(-2)-\frac{(-2)^2}{-2-1}$

$f(-2)=-6-\frac{4}{-3}$

$f(-2)=\frac{18}{-3}-\frac{4}{-3}$

$f(-2)=\frac{18-4}{-3}$

$f(-2)=-\frac{14}{3}$

Step 3: Substitute the function value of the inside portion into .

$h\left(-\frac{14}{3} \right )=2\left(-\frac{14}{3} \right )-3$

$h\left(-\frac{14}{3} \right )=\left(-\frac{28}{3} \right )-3$

$h\left(-\frac{14}{3} \right )=-\frac{28}{3}-\frac{9}{3}$

$h\left(-\frac{14}{3} \right )=-\frac{37}{3}$

$h(f(-2))=-\frac{37}{3}$

Compare your answer with the correct one above

Question

Calculate for the following function .

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is six.

$f(6)\rightarrow x=6$

Step 2: Given the function, input the desired value.

In step one the input value of six was found. Now substitute 6 in for every in the function.

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(6)=24$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Calculate the function value of for .

$f(x)=x+\frac{x^2}{x^2-1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is one.

$f(1)\rightarrow x=1$

Step 2: Given the function, input the desired value.

In step one the input value of one was found. Now substitute 1 in for every in the function.

$f(x)=x+\frac{x^2}{x^2-1}$

$f(1)=1+\frac{1^2}{1^2-1}$

$f(1)=1+\frac{1}{0}$

Since a fraction cannot have a zero in the denominator, the function value at does not exist.

Step 3: Verify solution by graphing function.

Recall that graphically, a vertical asymptote represents where the function does not exist.

Looking at the above graph the function does not exist at $x=\pm1$ thus verifying the solution found in step 2.

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Question

For the given function , calculate .

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is two.

$f(2)\rightarrow x=2$

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function.

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(2)=7$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Given the function , find the function value when is four.

$f(x)=16-2x+\frac{x}{4}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is four.

$f(4)\rightarrow x=4$

Step 2: Given the function, input the desired value.

In step one the input value of four was found. Now substitute 4 in for every in the function.

$f(x)=16-2x+\frac{x}{4}$

$f(4)=16-2(4)+\frac{4}{4}$

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(4)=9$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Given the following functions and , calculate the composition .

$g(x)=x-\frac{4x}{x^2}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form and the question asks to calculate we know that the input value is two.

$g(2)\rightarrow x=2$

After the function value of is calculated, it will be the input value for .

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function .

$g(x)=x-\frac{4x}{x^2}$

$g(2)=2-\frac{4(2)}{2^2}$

$g(2)=2-\frac{4(2)}{2^2}$

$g(2)=2-\frac{8}{4}$

Step 3: Substitute the function value of the inside portion into .

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Question

For the function , calculate the function value at negative five.

$f(x)=5x-\frac{100-x}{5}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is negative five.

$f(-5)\rightarrow x=-5$

Step 2: Given the function, input the desired value.

In step one the input value of negative five was found. Now substitute -5 in for every in the function.

$f(x)=5x-\frac{100-x}{5}$

$f(-5)=5(-5)-\frac{100--5}{5}$

$f(-5)=-25-\frac{105}{5}$

$f(-5)=-25-\frac{21\cdot 5}{5}$

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Question

Given the following function , calculate .

$f(x)=\frac{1}{x}+\sqrt{3x-5}$

Assume is always positive.

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.Math.content.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is three.

$f(3)\rightarrow x=3$

Step 2: Given the function, input the desired value.

In step one the input value of three was found. Now substitute 3 in for every in the function.

$\f(x)=\frac{1}{x}+\sqrt{3x-5} \ \f(3)=\frac{1}{3}+\sqrt{3(3)-5} \ \ f(3)=\frac{1}{3}+\sqrt{9-5} \ \f(3)=\frac{1}{3}+\sqrt{4} \ \f(3)=\frac{1}{3}+ 2 \ \f(3)=\frac{7}{3}$

Step 3: Answer the question.

The answer is

$f(3)=\frac{7}{3}$

Compare your answer with the correct one above

Question

Given the following function , calculate .

$g(x)=\frac{x^2-3}{x^3+1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is two.

$g(2)\rightarrow x=2$

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function.

$g(x)=\frac{x^2-3}{x^3+1}$

$g(2)=\frac{2^2-3}{2^3+1}$

$g(2)=\frac{2^2-3}{2^3+1}$

$g(2)=\frac{4-3}{8+1}$

$g(2)=\frac{1}{9}$

Step 3: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

$g(2)=\frac{1}{9}$

Compare your answer with the correct one above

Question

Given the following functions and , calculate .

$\f(x)=3x+2 \g(x)=x^2-2x+1$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form and the question asks to calculate we know that the input value is two.

$f(2)\rightarrow x=2$

After the function value of is calculated, it will be the input value for .

Step 2: Given the function, input the desired value.

In step one the input value of two was found. Now substitute 2 in for every in the function .

$\ f(2)=3(2)+2 \f(2)=6+2 \f(2)=8$

Step 3: Substitute the function value of the inside portion into .

$\g(x)=x^2-2x+1 \g(8)=8^2-2(8)+1 \g(8)=64-16+1 \g(8)=49$

Compare your answer with the correct one above

Question

Given the following function , calculate .

$f(x)=\frac{x^2-10}{x}+2x$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is five.

$f(5)\rightarrow x=5$

Step 2: Given the function, input the desired value.

In step one the input value of five was found. Now substitute 5 in for every in the function.

$f(x)=\frac{x^2-10}{x}+2x$

$f(5)=\frac{5^2-10}{5}+2(5)$

$f(5)=\frac{25-10}{5}+10$

$f(5)=\frac{15}{5}+10$

Step 3: Verify solution by graphing function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(5)=13$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Calculate for the function .

$f(x)=x-\frac{1}{2x+3}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is negative three.

$f(-3)\rightarrow x=-3$

Step 2: Given the function, input the desired value.

In step one the input value of negative three was found. Now substitute negative three in for every in the function.

$f(x)=x-\frac{1}{2x+3}$

$f(-3)=-3-\frac{1}{2(-3)+3}$

$f(-3)=-3-\frac{1}{-6+3}$

$f(-3)=-3-\frac{1}{-3}$

$f(-3)=\frac{9}{-3}-\frac{1}{-3}$

$f(-3)=\frac{9-1}{-3}$

$f(-3)=-\frac{8}{3}$

Step 3: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

$f(-3)=-\frac{8}{3}$ .

Compare your answer with the correct one above

Question

Calculate .

$f(x)=3x-\frac{x^2}{x-1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the inside function is in the form and the question asks to calculate we know that the input value is negative two.

$f(-2)\rightarrow x=-2$

After the function value of is calculated, it will be the input value for .

Step 2: Given the function, input the desired value.

In step one the input value of negative two was found. Now substitute -2 in for every in the function .

$f(x)=3x-\frac{x^2}{x-1}$

$f(-2)=3(-2)-\frac{(-2)^2}{-2-1}$

$f(-2)=-6-\frac{4}{-3}$

$f(-2)=\frac{18}{-3}-\frac{4}{-3}$

$f(-2)=\frac{18-4}{-3}$

$f(-2)=-\frac{14}{3}$

Step 3: Substitute the function value of the inside portion into .

$h\left(-\frac{14}{3} \right )=2\left(-\frac{14}{3} \right )-3$

$h\left(-\frac{14}{3} \right )=\left(-\frac{28}{3} \right )-3$

$h\left(-\frac{14}{3} \right )=-\frac{28}{3}-\frac{9}{3}$

$h\left(-\frac{14}{3} \right )=-\frac{37}{3}$

$h(f(-2))=-\frac{37}{3}$

Compare your answer with the correct one above

Question

Calculate for the following function .

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is six.

$f(6)\rightarrow x=6$

Step 2: Given the function, input the desired value.

In step one the input value of six was found. Now substitute 6 in for every in the function.

Step 3: Verify solution by graphing the function.

To find the function value on a graph go to and find the y value that lies on the graph at . Looking at the graph above when , .

Recall that $f(x)=y \rightarrow f(6)=24$ , thus verifying the solution found in step 2.

Compare your answer with the correct one above

Question

Calculate the function value of for .

$f(x)=x+\frac{x^2}{x^2-1}$

Answer

This question is testing the knowledge and skills of calculating a function value. Similar to domain and range, calculating the function value requires the application of input values into the function to find the output value. In other words, evaluating a function at a particular value results in the function value; which is another way of saying function value is the output.

For the purpose of Common Core Standards, function notation and evaluation fall within the Cluster A of the function and use of function notation concept (CCSS.MATH.CONTENT.HSF-IF.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the input value.

Since the function is in the form and the question asks to calculate we know that the input value is one.

$f(1)\rightarrow x=1$

Step 2: Given the function, input the desired value.

In step one the input value of one was found. Now substitute 1 in for every in the function.

$f(x)=x+\frac{x^2}{x^2-1}$

$f(1)=1+\frac{1^2}{1^2-1}$

$f(1)=1+\frac{1}{0}$

Since a fraction cannot have a zero in the denominator, the function value at does not exist.

Step 3: Verify solution by graphing function.

Recall that graphically, a vertical asymptote represents where the function does not exist.

Looking at the above graph the function does not exist at $x=\pm1$ thus verifying the solution found in step 2.

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