Common Core: High School - Functions : Graph Rational Functions, Identify Zeros, Asymptotes, and End Behavior: CCSS.Math.Content.HSF-IF.C.7d

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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 Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the following function and its asymptotes.

Possible Answers:

Screen shot 2016 01 13 at 12.58.06 pm

Screen shot 2016 01 13 at 12.43.56 pm

Screen shot 2016 01 13 at 12.43.56 pm

Screen shot 2016 01 13 at 12.58.06 pm

Screen shot 2016 01 13 at 1.00.17 pm

Correct answer:

Screen shot 2016 01 13 at 12.43.56 pm

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Screen shot 2016 01 13 at 12.43.56 pm

Example Question #2 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question2

Screen shot 2016 01 13 at 12.43.56 pm

Screen shot 2016 01 13 at 12.43.56 pm

Screen shot 2016 01 13 at 12.58.06 pm

Screen shot 2016 01 13 at 12.58.06 pm

Correct answer:

Question2

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question2

Example Question #3 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question3

Screen shot 2016 01 13 at 1.00.17 pm

Question2

Screen shot 2016 01 13 at 12.43.56 pm

Screen shot 2016 01 13 at 12.58.06 pm

Correct answer:

Question3

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question3

Example Question #4 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question2

Question4

Screen shot 2016 01 13 at 1.00.17 pm

Screen shot 2016 01 13 at 12.58.06 pm

Question3

Correct answer:

Question4

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question4

Example Question #5 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question5

Question3

Screen shot 2016 01 13 at 12.58.06 pm

Question2

Question4

Correct answer:

Question5

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

 

Question5

Example Question #6 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question3

Question2

Question6

Question5

Question4

Correct answer:

Question6

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question6

Example Question #7 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question5

Question4

Question7

Question6

Question3

Correct answer:

Question7

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question7

Example Question #8 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question8

Question6

Question4

Question7

Question5

Correct answer:

Question8

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question8

Example Question #9 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question8

Question2

Question9

Question5

Question6

Correct answer:

Question9

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

Recall that when n is some large value, the fraction approaches zero.

Therefore, the horizontal asymptote is at .

Step 3: Graph the function using technology and plot the asymptotes.

Question9

Example Question #10 : Graph Rational Functions, Identify Zeros, Asymptotes, And End Behavior: Ccss.Math.Content.Hsf If.C.7d

Graph the function and its asymptotes.

Possible Answers:

Question9

Question10

Question8

Question6

Question5

Correct answer:

Question10

Explanation:

This question is testing one's ability to graph a rational function and identify its asymptotes.

For the purpose of Common Core Standards, "graph rational functions, identifying zeros and asymptotes 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 identify asymptotes of the function.

Recall that asymptotes occur at locations where the domain and range of the function do not exist. For vertical asymptotes this occurs if there is a fraction where the denominator contains the variable:

Given the function

thus a vertical asymptote is at .

Step 2: Identify the horizontal asymptote by examining the end behavior of the function.

Given the function

to find the end behavior, substitute in large values for x. When large values of x are put into the function the denominator becomes larger. 

This particular case has  and has a range of all reals therefore, there is no horizontal asymptote.

Step 3: Graph the function using technology and plot the asymptotes.

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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