Precalculus : Graph a Polynomial Function

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Graph A Polynomial Function

 

Which of the following is an accurate graph of ?

Possible Answers:

Varsity1

Varsity10

Varsity2

Varsity11

Varsity12

Correct answer:

Varsity1

Explanation:

is a parabola, because of the general  structure.  The parabola opens downward because .  

Solving tells the x-value of the x-axis intercept;

The resulting x-axis intercept is: .

Setting  tells the y-value of the y-axis intercept;

    

    

    

The resulting y-axis intercept is:

Example Question #1 : How To Graph An Exponential Function

Give the -intercept of the graph of the function

Round to the nearest tenth, if applicable.

Possible Answers:

The graph has no -interceptx

Correct answer:

Explanation:

The -intercept is , where :

The -intercept is .

Example Question #1 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the following function and identify the zeros.

Possible Answers:

Screen shot 2016 01 13 at 9.50.10 am

Screen shot 2016 01 13 at 12.17.10 pm

Screen shot 2016 01 13 at 9.55.24 am

 

Screen shot 2016 01 13 at 12.16.31 pm

Screen shot 2016 01 13 at 12.16.52 pm

Correct answer:

Screen shot 2016 01 13 at 9.55.24 am

 

Explanation:

This question tests one's ability to graph a polynomial function.

For the purpose of Common Core Standards, "graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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: Use algebraic technique to factor the function.

Separating the function into two parts...

Factoring a negative one from the second set results in...

Factoring out  from the first set results in...

The new factored form of the function is,

.

Now, recognize that the first binomial is a perfect square for which the following formula can be used

since 

thus the simplified, factored form is,

.

Step 2: Identify the roots of the function.

To find the roots of a function set its factored form equal to zero and solve for the possible x values.

Step 3: Create a table of  pairs.

The values in the table are found by substituting in the x values into the function as follows.

Step 4: Plot the points on a coordinate grid and connect them with a smooth curve.

Screen shot 2016 01 13 at 9.55.24 am

 

Example Question #1 : Graph A Polynomial Function

Graph the function and identify the roots.

Possible Answers:

Question6

Question3

Question2

Question5

Question12

Correct answer:

Question12

Explanation:

This question tests one's ability to graph a polynomial function.

For the purpose of Common Core Standards, "graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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: Use algebraic technique to factor the function.

Recognize that the binomial is a perfect square for which the following formula can be used

since 

thus the simplified, factored form is,

.

Step 2: Identify the roots of the function.

To find the roots of a function set its factored form equal to zero and solve for the possible x values.

        

Step 3: Create a table of  pairs.

The values in the table are found by substituting in the x values into the function as follows.

Step 4: Plot the points on a coordinate grid and connect them with a smooth curve.

Question12

Example Question #1 : Graphs Of Polynomial Functions

Graph the function and identify its roots.

Possible Answers:

Question5

Question6

Question4

Question3

Screen shot 2016 01 13 at 12.16.31 pm

Correct answer:

Question6

Explanation:

This question tests one's ability to graph a polynomial function.

For the purpose of Common Core Standards, "graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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: Use algebraic technique to factor the function.

Recognize that the binomial is a perfect square for which the following formula can be used

since 

thus the simplified, factored form is,

.

Step 2: Identify the roots of the function.

To find the roots of a function set its factored form equal to zero and solve for the possible x values.

        

Step 3: Create a table of  pairs.

The values in the table are found by substituting in the x values into the function as follows.

Step 4: Plot the points on a coordinate grid and connect them with a smooth curve.

Question6

Example Question #2 : Graphs Of Polynomial Functions

Graph the function and identify its roots.

Possible Answers:

Screen shot 2016 01 13 at 12.16.31 pm

Question3

Screen shot 2016 01 13 at 12.16.52 pm

Question4

Question2

Correct answer:

Question4

Explanation:

This question tests one's ability to graph a polynomial function.

For the purpose of Common Core Standards, "graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7). 

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: Use algebraic technique to factor the function.

Recognize that the binomial is a perfect square for which the following formula can be used

since 

thus the simplified, factored form is,

.

Step 2: Identify the roots of the function.

To find the roots of a function set its factored form equal to zero and solve for the possible x values.

        

Step 3: Create a table of  pairs.

The values in the table are found by substituting in the x values into the function as follows.

Step 4: Plot the points on a coordinate grid and connect them with a smooth curve.

Question4

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