Characteristics of Rational Functions

Characteristics of Rational Functions

Multiple Choice

What is a rational function?

 $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$  

• A function where x has a rational exponent

• A ratio of 2 functions

• A quadratic function

• A function that is easy to solve

Multiple Choice

I Do:

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

We Do:

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

You Do:

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

Multiple Choice

We Do:

What is the domain of the function?

• x=2

• x $\ne$ 2

• x>2

• x<2

Multiple Select

You Do:

In finding the domain of the rational function

 $r\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$  where p(x) and q(x) are polynomial functions, all real numbers are allowed for x except . . .
(Check all that applies.)

• The ones that would make the numerator zero. $p\left(x\right)=0$  

• The ones that would make the denominator zero.  $q\left(x\right)=0$  

• The ones that would make the function zero. $r\left(x\right)=0$  

• The ones that would make the function undefined.

Multiple Choice

You Do:

Find the range of 

 $y=\frac{2}{x+1}$  .

•  $y\ne-1$  

•  $y\ne0$  

•  $y\ne1$  

•  $y\ne2$  

Multiple Choice

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

• vertical
• horizontal
• slant
• none

Multiple Choice

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3

Multiple Choice

What is the hole?

• x= 4
• x= -4
• x= 5
• x= -5

Multiple Choice

What are the zero(s) of

 $\frac{x^2-6x-16}{x+5}$  

• x = 8 and x = -2

• x = 8, x = -2 and x = -5

• x = -8 and x = 2

• x = -5

Multiple Choice

Find the horizontal asymptote.

• None
• y = 0
• y = -1/3
• y = -3

Multiple Choice

When finding the Horizontal asymptotes of a function, you should be thinking...

• "Set Bottom = to Zero"
• "Top = 0"
• "f(0)"
• "Look at the Degree of the top and bottom..."

Multiple Choice

I Do:

Where is there a hole on the graph of the function?

• x = 2

• x = -2

• There are no holes.

• x = 5

Multiple Choice

We Do:

Find the hole of the function.

x²- 9x+20

___________

4x² - 12x- 40

• x =5

• x=0

• x=4

• x=-2

Multiple Choice

You Do:

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: x = -3;

  VA: x = 1

• Holes: x = -3, 1

  VA: None

• Holes: x = 1

  VA: x = -3