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

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Given the following functions  and , calculate .

 

Possible Answers:

Correct answer:

Explanation:

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.

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 .

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

 

Example Question #1 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Given the following function , calculate .

Possible Answers:

Correct answer:

Explanation:

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.

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: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

Example Question #3 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Calculate .

Possible Answers:

Correct answer:

Explanation:

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.

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 .

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

Example Question #2 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Calculate  for the function .

Possible Answers:

Correct answer:

Explanation:

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.

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.

Step 3: Answer the question.

This particular function when solved algebraically results in one value.

The answer is

.

Example Question #3 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Calculate  for the following function .

Possible Answers:

Correct answer:

Explanation:

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.

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.


Screen shot 2016 01 08 at 11.04.06 am

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 , thus verifying the solution found in step 2.

Example Question #4 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Given the following function , calculate .

Possible Answers:

Correct answer:

Explanation:

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.

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.

Step 3: Verify solution by graphing function.

Screen shot 2016 01 08 at 10.25.41 am

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 , thus verifying the solution found in step 2.

Example Question #7 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Calculate the function value of  for .

Possible Answers:

Correct answer:

Explanation:

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.

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.

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.

Screen shot 2016 01 08 at 11.16.44 am

Looking at the above graph the function does not exist at  thus verifying the solution found in step 2.

Example Question #5 : Function Notation: Ccss.Math.Content.Hsf If.A.2

For the given function , calculate .

 

Possible Answers:

Correct answer:

Explanation:

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.

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.

Screen shot 2016 01 08 at 11.24.05 am

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 , thus verifying the solution found in step 2.

Example Question #9 : Function Notation: Ccss.Math.Content.Hsf If.A.2

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

Possible Answers:

Correct answer:

Explanation:

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.

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.

Step 3: Verify solution by graphing the function.

Screen shot 2016 01 08 at 12.21.20 pm

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 , thus verifying the solution found in step 2.

Example Question #6 : Function Notation: Ccss.Math.Content.Hsf If.A.2

Given the following functions  and , calculate the composition .

Possible Answers:

Correct answer:

Explanation:

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.

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 .

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

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept
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