Unit 4 Day 4: Transforming Rational Functions

Quadratic Function

Rational Function 

Absolute Value Function 

Cubic Function

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

-f(x)

f(-x)

f^-1(x)

f(2x)

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

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

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

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

$$x=-4,\ x=2$$  

$$x=-2,\ x=4$$  

$$x=-6,\ x\ =\ -2$$  

$$x=\ 2,\ x=6$$  

$$y=\frac{3}{4}$$  

$$y=\frac{4}{3}$$  

$$y=0$$  

No asymptote

$$y=4$$  

$$y=\frac{1}{4}$$  

$$y=0$$  

No Asymptote

TRUE

FALSE

$$x=2,3$$  

$$x=-3,-2$$  

$$x=-3,1$$  

None

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

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

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

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

TRUE

FALSE

$$x=-9,-1$$  

$$x=1,9$$  

$$x=3$$  

None