Common Core: High School - Functions : Graph Polynomial Functions, Identify Zeros, Factor, and Identify End Behavior.: CSS.Math.Content.HSF-IF.C.7c

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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 : 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 12.16.52 pm

Screen shot 2016 01 13 at 9.50.10 am

Screen shot 2016 01 13 at 9.55.24 am

 

Screen shot 2016 01 13 at 12.17.10 pm

Screen shot 2016 01 13 at 12.16.31 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 Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify its roots.

Possible Answers:

Question2

Screen shot 2016 01 13 at 12.16.31 pm

Question4

Screen shot 2016 01 13 at 9.50.10 am

Question3

Correct answer:

Question2

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.

Question2

Example Question #3 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify the roots.

Possible Answers:

Question2

Question4

Screen shot 2016 01 13 at 12.16.52 pm

Question3

Screen shot 2016 01 13 at 9.50.10 am

Correct answer:

Question3

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.

Question3

Example Question #2 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify its roots.

Possible Answers:

Question3

Screen shot 2016 01 13 at 12.16.52 pm

Question2

Question4

Screen shot 2016 01 13 at 12.16.31 pm

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

Example Question #3 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify its roots.

Possible Answers:

Question2

Question4

Screen shot 2016 01 13 at 9.50.10 am

Question5

Question3

Correct answer:

Question5

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.

Question5

Example Question #4 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify its roots.

Possible Answers:

Question6

Question3

Question5

Screen shot 2016 01 13 at 12.16.31 pm

Question4

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

Graph the function and identify the roots.

Possible Answers:

Question7

Question6

Question5

Question4

 

Question2

Correct answer:

Question7

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.

Question7

Example Question #5 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify the roots.

Possible Answers:

Question8

Question4

Question6

Question5

Question7

Correct answer:

Question8

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.

Question8

Example Question #9 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify the roots.

Possible Answers:

Question8

Question9

Question3

Question4

Question7

Correct answer:

Question9

Explanation:

his 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 techniques to solve for the roots.

Step 2: Create a table of  pairs.

Step 3: 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.

Question9

Example Question #10 : Graph Polynomial Functions, Identify Zeros, Factor, And Identify End Behavior.: Css.Math.Content.Hsf If.C.7c

Graph the function and identify the roots.

Possible Answers:

Question7

Question9

Question8

Question10

Question5

Correct answer:

Question10

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.


Question10

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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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