Vertical and Horizontal Rational Functions Review

Review - Unit Test: Rational Functions

Inverse Variation

 $y=\frac{k}{x}$  

Multiple Choice

If y varies inversely as x, and y = 23 when x = 8, find y when x = 4.

• 26

• 46

• 52

• 92

Multiple Choice

Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.

• 300
• 75
• 1,875
• 12

Multiple Choice

The volume V of a gas kept at a constant temperature varies inversely as the pressure p.
If the pressure is 24 pounds per square inch, the volume is 15 cubic feet.
What will be the volume when the pressure is 30 pounds per square inch?

• 8 cubic feet
• 10 cubic feet
• 12 cubic feet
• 14 cubic feet

Transformations of Rational Functions

 $y=\frac{a}{x-h}+k$  

Multiple Choice

How is this function transformed from the parent function?

• Translated left and up
• Translated right and up
• Translated left and down
• Translated right and down

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which functions shifts left 6 units?

• F(x) =  $$\frac{1}{x}-6$$  

• F(x) = $$\frac{1}{x\ -6}$$  

• F(x) =  $$\frac{1}{x}\ +6$$  

• F(x) =  $$\frac{1}{x+6}$$  

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which function shifts up 3 units?

• F(x) =  $$\frac{1}{x+3}$$  

• F(x) =  $$\frac{1}{x-3}$$  

• F(x) =  $$\frac{1}{x}+3$$  

• F(x) = $$\frac{1}{x}-3$$  

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which function shifts right 10 units and down 4 units?

• F(x) =  $$\frac{1}{x-10}-4$$  

• F(x) =  $$\frac{1}{x+10}+4$$  

• F(x) =  $$\frac{1}{x-4}+10$$  

• F(x) =  $$\frac{1}{x+4}-10$$  

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which function shifts down 6 units?

• F(x) = $$\frac{1}{x-6}$$  

• F(x) = $$\frac{1}{x}-6$$  

• F(x) = $$\frac{1}{x+6}$$  

• F(x) = $$\frac{1}{x}+6$$  

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x+2}-5$$  translate?

• Shifts left 2 units and up 5 units.

• Shifts right 2 units and up 5 units.
  

• Shifts right 2 units and down 5 units.

• Shifts left 2 units and down 5 units.

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  how does f(x) =   $$\frac{1}{x-4}+1$$ Translate. 

• Shifts left 4 units and up 1 unit.

• Shifts left 4 units and down 1 unit.
  

• Shifts right 4 units and up 1 unit.
  

• Shifts right 4 units and down 1 unit.

Multiple Choice

Referring to f(x)=  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x}+3$$  translate?

• Shifts right 3 units.

• Shifts up 3 units.

• Shifts left 3 units.

• Shifts down 3 units.

Multiple Choice

Referring to f(x)=  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x+3}$$  translate?. 

• Shifts right 3

• Shifts up three

• Shifts left three

• Shifts down three

Vertical Asymptotes of Rational Functions

Set the denominator equal to zero and solve for x.

Multiple Choice

Find the vertical asymptote(s).

• None
• x = 0
• x= 4
• x = -4, 4

Multiple Select

Find the vertical asymptote.

$$g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}$$  

• x=-5

• x=1/2

• x=-1/2

• x=-3

• x=2

Multiple Choice

Which of the following is determined by just looking at the denominator?

• vertical asymptote
• horizontal asymptote
• holes
• slant asymptote

Multiple Choice

Find the vertical asymptote.

$$f\left(x\right)=\frac{x^2-2x-8}{3x-2}$$  

• y=2/3

• x=3/2

• x= 2/3

• x=1/3

Multiple Choice

State the vertical asymptote.

• x = -2/5

• x = -5/2

• x = -5

• x = 2

Multiple Choice

What is the Vertical Asymptotes?

• x= -4

• x= -4,5

• x= -5,5

• x= 4

Multiple Choice

What is the Vertical Asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

Multiple Choice

What is/are the vertical asymptote(s)?

• x=-2
• x=2 and x=3
• x=-3
• x=3

Multiple Select

 What is the vertical(s) asymptote of the function: $$f\left(x\right)=\frac{x-1}{x^2-144}$$

• x=12

• x=-12

• x=144

• x=72

• x=-72

Horizontal Asymptotes

Rules

• N<D, H.A.: y=0

• N>D, no H.A.

• N=D, H.A.: y=a/b where a and b are the leading coefficients.

Multiple Choice

The horizontal asymptote equals zero when:

• the degree of the numerator and denominator are equal

• the degree of the numerator is less than the degree of the denominator

• the degree of the numerator is greater than the degree of the denominator

• the numerator equals zero

Multiple Choice

What is the horizontal asymptote of this function?

• y=2
• x=1/2
• y=1
• y=1/2

Multiple Choice

Find the horizontal asymptote.

• None
• y=-2
• y=2
• y=0

Multiple Choice

• y = 0
• y = 1/2
• y = 2
• None

Multiple Choice

What is the horizontal asymptote?

• y = -4
• y = 1
• x = 1
• y = -6

Multiple Choice

What is the horizontal asymptote to this function?

• y=4
• y=0
• y=-2
• y=1

Mixed Asymptotes

Multiple Choice

Which of the following represents the graph below?

Multiple Choice

• All Reals Except 0
• All Reals
• All Reals Except -3
• All Reals Except 0 and -3

Multiple Choice

What is the vertical asymptote? 

• x = 2
• x = 7
• y = 2
• y = 7

Multiple Choice

What is the domain and range?

• D : All real number x ≠ -3
  R: All real number y≠ 1
• D : All real number x ≠ 1
  R: All real number y≠ -3
• D : All real number x ≠ 3
  R: All real number y≠ 1
• D : All real number x ≠ -1
  R: All real number y≠ 3

Multiple Choice

What is the horizontal asymptote? 

• x = 2
• x = 7
• y = 2
• y = 7

Multiple Choice

Which is the graph of the rational equation:

Multiple Choice

Find the domain of the function. $$f(x)=\frac{x}{2x+4}$$  

• x cannot equal to 2

• x cannot equal to 1/2

• x cannot equal to -2

• All real numbers

Multiple Choice

Find the domain of the function. $$f(x)=\frac{x^3}{x+8}$$  

• x cannot equal to 8

• x cannot equal to 0

• x cannot equal to -8

• All real numbers

Multiple Choice

What are the asymptotes?

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

Multiple Choice

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

Multiple Choice

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

Multiple Choice

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

Multiple Choice

What are the asymptotes?

• x=1, x= 2, y =1, y= 2
• x= 2, x=-2, y = 1
• x=2 y =-1
• x=1 y =2, y =-2

Slant or Oblique Asymptotes

Use Long Division

Multiple Choice

Identify the Oblique Asymptote for this function.

• y = 5x - 7

• y = 5x + 13

• y = 5x + 3

• y = 5x + 7

Multiple Choice

What is the oblique asymptote for the function?

• y = 12

• y = x - 5

• y = x-5 + 12/(x+2)

• y = 12/(x+2)

Multiple Choice

Find the oblique asymptote.
(x² - 2x - 8) / (x - 2)

• y = x
• y = x - 8
• y = x - 4
• y = x + 4

Multiple Choice

What is the slant (Oblique) asymptote for the equation

f(x) = (x² - 4x + 2)/(x + 3)

• y = x -1

• y = x -7

• y = -7x + 23

• y = -2x + 2