Final Exam Review: Unit 3 (Rational Functions)

​Unit 3: Rational Functions

• Identify the major characteristics of a rational function.

  • X-intercept(s)

  • Y-intercept

  • Horizontal Asymptote (BOT, Same, BOB)

  • Vertical Asymptote(s)

  • Slant Asymptote

  • Hole(s)

• State the domain and range of a rational function

• Graph rational functions

​Link to Notes

Multiple Choice

What is the equation of the horizontal asymptote?

• y = 0

• y = -2

• y = 2

• There isn't one

Multiple Choice

• y = 0
• $$y=\frac{1}{2}$$  

• y = 2
• None

Multiple Choice

Find the horizontal asymptote.

• None
• y = -2

• y = 2

• y = 0

Multiple Choice

Which asymptote(s) are determined by looking at the denominator?

• vertical
• horizontal
• slant
• none

Multiple Choice

What are the domain and range?

• D : $$\left(-\infty,-3\right)\cup\left(-3,\infty\right)$$ R: $$\left(-\infty,1\right)\cup\left(1,\infty\right)$$

• D : $$\left(-\infty,1\right)\cup\left(1,\infty\right)$$ R: $$\left(-\infty,-3\right)\cup\left(-3,\infty\right)$$

• D : $$\left(-\infty,3\right)\cup\left(3,\infty\right)$$ R: $$\left(-\infty,-1\right)\cup\left(-1,\infty\right)$$  

• D: $$\left(-\infty,-1\right)\cup\left(-1,\infty\right)$$ R: $$\left(-\infty,3\right)\cup\left(3,\infty\right)$$

Multiple Choice

Which rational function has a vertical asymptote at x = -3

• $$y=\frac{1}{x-3}$$  

• $$y=\frac{1}{x+3}$$  

• $$y=\frac{1}{3}$$  

• $$y=\frac{3}{x}$$  

Multiple Choice

A vertical asymptote is found by setting the _________ (of reduced function) equal to zero and solving for x 

• Numerator
• Denominator
• Right side 
• Left side

Multiple Choice

Solve for the y-intercept: $$f\left(x\right)=\frac{x-2}{x^2-5x+6}$$

• (0,2)

• -6, 1

• $$\ \frac{1}{3}$$

• $$\left(0,-\frac{1}{3}\right)$$

Math Response

Solve for the slant asymptote. (Enter answer in y=mx+b form) $$f\left(x\right)=\frac{x^2-3x-4}{x+3}$$

Type answer here

Correct Answer: y=x-6

Deg^°

Rad

Multiple Choice

What is the domain of a rational function?

• All real numbers

• All real numbers except where the denominator is zero

• Only positive real numbers

• Only negative real numbers

Multiple Choice

What are the vertical asymptotes of...

• x = 0, -5
• x=0, 5
• x = 2, -7
• x = -2, 7

Multiple Choice

What is the vertical asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

Multiple Choice

What is/are the x-intercepts of this graph?

• (-2,0) and (2,0)
• (-2,0)
• (3,0)
• (2,0) and (3,0

Multiple Choice

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.

Multiple Choice

Find the equation of the vertical asymptote(s) of f(x).

• x = -5

• x = -5 and x = -3

• y = 0

• x = -3

Multiple Choice

Find the vertical asymptote(s) of f(x).

• x = -5 and x = 7

• x = 3 and x = 4

• x = 3 and x = -5

• There are no vertical asymptotes

Multiple Choice

True or False: There is a hole in f(x).

• True

• False

Multiple Choice

What is the vertical asymptote(s) of the function?

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

• x=-1/2 and x=3

• x=-1/2

• x=1/2 and x = -3

• x=1/2

Multiple Choice

What is the x-intercept(s) of the rational function?

$$y\ =\ \frac{\left(x+7\right)\left(x-4\right)}{\left(3x+1\right)\left(x+4\right)}$$  

• x=7 and x = -4

• x = 7

• x = -7

• x = -7 and x = 4

Multiple Choice

What is the hole in the function?

$$y\ =\ \frac{\left(x+9\right)\left(x\ +\ 3\right)}{\left(x+4\right)\left(x+3\right)}$$  

• No hole

• $$\left(3,\ \frac{12}{7}\right)$$  

• $$\left(-3,\ 6\right)$$  

• $$\left(-3,\ -6\right)$$  

Multiple Choice

What is the horizontal asymptote for the function?

$$y\ =\ \frac{5x^2+3}{x^2+4x}$$  

• No horizontal Aysmptote

• y = 5

• y = 1/5

• y = 0

Multiple Choice

The rational function, $$y=\frac{1}{x-5}$$  is undefined at...

• x = 1

• x = 5

• x = -5

• x = 0