Unit 4 Day 4: Transforming Rational Functions

Review: Transforming Rational Functions

Today

• Work through this Quizizz (take notes!)

• Review notes (from last class and the quizizz)

• Take Skills Check: Transforming Rational Functions

Multiple Choice

What is the name of this function?

• Quadratic Function

• Rational Function 

• Absolute Value Function 

• Cubic Function

Multiple Choice

What are the transformations from the parent function y=x²?

y=3(x-4)²?

• vertical stretch by a factor of 3, horizontal shift right by 4

• horizontal shift left by 4, vertical stretch by a factor of 3

• horizontal shift right by 4, vertical stretch by a factor of 1/3

• horizontal shift right by 4, vertical shift up 3

Multiple Choice

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)

• f(-x)

• f^-1(x)

• f(2x)

Multiple Choice

Identify the transformations from the parent function g(x)=1/x.

• right 2, down 1, reflect over the x-axis

• right 2, down 1, reflect over the y-axis

• left 2, down 1, reflect over the y-axis

• left 2, up 1, reflect over the y-axis

Multiple Choice

Describe the transformations from the parent function g(x) = 1/x

• vertical compression by 3, right 7

• vertical stretch by 3, right 7

• vertical stretch by 3, up 7

• vertical compress by 1/3, up 7

Multiple Choice

Describe all transformations from the parent function g(x)=1/x to f(x).

• Shift right 5 and shift up 7

• Shift left 7 and shift up 5

• Reflect over the x-axis, shift up 7

• Shift left 5 and shift up 7

Multiple Choice

Describe the transformations from the parent function g(x) =1/x

• reflection over the x-axis, right 2, down 4

• reflection over the y-axis, right 2 down 4

• reflection over the x-axis, left 2, down 4

• reflection over the y-axis, left 2, down 4

Rational Functions

Finding Vertical Asymptotes

Multiple Choice

Find the Vertical Asymptotes for the following function

$$g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}$$  

• $$x=-4,\ x=2$$  

• $$x=-2,\ x=4$$  

• $$x=-6,\ x\ =\ -2$$  

• $$x=\ 2,\ x=6$$  

Finding Horizontal Asymptotes

Finding Horizontal Asymptotes

Finding Horizontal Asymptotes

Multiple Choice

What is the horizontal asymptote of the following function?

$$f\left(x\right)=\frac{3x^2}{4x^2-1}$$  

• $$y=\frac{3}{4}$$  

• $$y=\frac{4}{3}$$  

• $$y=0$$  

• No asymptote

Multiple Choice

What is the horizontal asymptote for the following function?

$$f\left(x\right)=\frac{4x+3}{x^2-4}$$  

• $$y=4$$  

• $$y=\frac{1}{4}$$  

• $$y=0$$  

• No Asymptote

Multiple Choice

To find the domain and vertical asymptotes, you set the bottom of the function equal to zero.

• TRUE

• FALSE

Multiple Choice

Find the vertical asymptotes of the function:

$$f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$$  

• $$x=2,3$$  

• $$x=-3,-2$$  

• $$x=-3,1$$  

• None

Multiple Choice

Find the domain of the function:

$$f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$$  

• $$D:\ \ all\ Real\ numbers,\ x\ne2,3$$  

• $$D:\ \ all\ Real\ numbers,\ x\ne-3,-2$$  

• $$D:\ \ all\ Real\ numbers,\ x\ne-3,1$$  

• $$D:\ \ all\ Real\ numbers,\ x\ne-1,3$$  

Multiple Choice

To find the x-intercepts, you set the bottom equal to zero.

• TRUE

• FALSE

Multiple Choice

Find the vertical asymptotes of the function:

$$f\left(x\right)=\frac{x^3-27}{x^2+10x+9}$$  

• $$x=-9,-1$$  

• $$x=1,9$$  

• $$x=3$$  

• None