Graphs of Rational Functions

​2.6 Rational Functions and Their Graphs

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Multiple Choice

A rational function in the form shown has #1

• x= h as its horizontal asymptote and y=k as its vertical asymptote

• x=h as its vertical asymptote and y=k as its horizontal asymptote

• x = -h as its horizontal asymptote and y=k as its vertical asymptote

• x = -h as its vertical asymptote and y=k as its horizontal asymptote

• Not sure what an asymptote is but I feel none of the answers listed are correct

Multiple Select

Which of the following represent(s) the domain of the function shown? #2

• x $$\ne$$  -3

• x $$\ne$$  3

• (- $$\infty$$  ,3) $$\cup$$  (3, $$\infty$$  )

• (- $$\infty$$  ,-3) $$\cup$$  (-3, $$\infty$$  )

• (- $$\infty$$  ,3] $$\cup$$  [3, $$\infty$$  )

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Multiple Choice

What are the vertical and horizontal asymptotes of the following function? #3

• vertical asymptote is 3 and horizontal asymptote is 1

• vertical asymptote is 1 and horizontal asymptote is 3

• vertical asymptote is 1 and horizontal asymptote is -3

• vertical asymptote is -1/3 and horizontal asymptote is 1

• vertical asymptote is 3 and horizontal asymptote is -1/3

Multiple Choice

What's the vertical asymptote of the function? #5

• x = 5

• x = 0

• x =5 , x = -5

• x = 25

Multiple Choice

What is the horizontal asymptote to this function? #6

• y=4
• y=0
• y=-2
• y=1

Multiple Choice

What is the domain of this function? #7

The dashed blue lines represent asymptotes

• $$\left(-\infty,\infty\right)$$  

• $$\left(-\infty,3\right)U\left(3,\infty\right)$$  

• $$\left(-\infty,3\right]$$  

• $$\left(-\infty,3\right)\left(4,\infty\right)$$  

Multiple Choice

What is the range of this function? #12

The dashed red lines represent asymptotes, and the open circle represents a hole in the graph.

• $$\left(-\infty,\infty\right)$$  

• $$\left(-\infty,1\right)U\left(1,\infty\right)$$  

• $$\left(-\infty,1\right)U\left(1,2\right)U\left(2,\infty\right)$$  

Multiple Choice

What is the domain and range of this rational function? #44

• D: $$\left(-\infty,\infty\right),\ x\ne4$$  

  R: $$\left(-\infty,\infty\right),\ y\ne0$$  

• D: $$\left(-\infty,\infty\right)$$  

  R: $$\left(-\infty,\infty\right)$$  

• D: $$\left(-\infty,4\right)$$  

  R: $$\left(-\infty,\infty\right)$$  

• D: $$\left(-\infty,\infty\right)$$  

  R: $$\left(-\infty,0\right)$$  

Multiple Choice

What are the asymptotes? #14

• x=-3, y=1
• x=3, y =1
• x=-3, y =-1
• x=3 y=-1

Multiple Choice

What is an asymptote? #18

• an imaginary line that your function never touches

• a part of your function

• a point on your graph

• a type of fruit

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Multiple Choice

What is the Vertical Asymptotes? #27

• x= -4
• x= -4,5
• x= -5,5
• x= 4

Multiple Choice

What is the domain? #28

• x≠ -5,5
• x≠ -5,4
• x≠ -4,5
• x≠ -4,-5

Multiple Choice

Does this function have any holes or zeros? If so, what are they? #34 $$y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$$  

• A hole when x = 4  No Zeros

• A hole when x =- 4   Zeros when: x = -3 and x = -7

• A hole when x = 4   Zeros when: x = -3 and x = -7

• A hole when x = 4   Zeros when x = 3 and x = 7