Transformations of Parent Functions
Name 3 types of Parent Functions
y=x
y=x2
y=sqrt(x)
y=|x|
ETC...
What variable are we looking at when we are talking about domain?
Domain is the x-values of a function that can be inputted into an equation.
What variable are we looking at when we are talking about range?
Range is the y-values of a function that can be outputted from an equation.
What are the three types of asymptotes?
Vertical Asymptotes
Horizontal Asymptotes
Oblique Asymptotes
What do we do when we take the inverse of a function?
We take the domain of the original and it is the range of the inverse
Then we take the range of the original function and it is the domain of the inverse.
If y=x is the parent function, then what is the function when you move 2 units up
y=x+2
What is the domain of
{(-3,7), (8,5), (1,2), (0,0)}
{-3, 0, 1, 8}
What is the range of
{(5,3), (1,2), (-7,-2), (-2,-9), (0,0)}
{-9, -2, 0, 2, 3}
Find the asymptotes of this function:
(x^2+12)/x
Vertical Asymptote: x=0
Horizontal Asymptote: None
Oblique Asymptote: y=x
What must we switch before we find the inverse of something algebraically?
Switch the y and the x and then solve for y
If y=x2 is the parent function, then what is the function when you move down 6 units, 2 units to the left and reflect over the x-axis
y=(-x+2)^2-6
What is the domain of the function
y= x2 + 3
Domain:
(-∞, ∞)
What is the Range of the function
y= x2 + 3
Range:
[3, ∞)
Find the asymptotes of this function:
y=(5x^2)/(x^2-16)
Vertical Asymptotes: x=-4, x=4
Horizontal Asymptote: y=5
Oblique Asymptote: None
What is the inverse function of
y= sqrt(x+2)
y=x2 -2
Describe the transformations in words:
3|x-2|+5
Horizontal Shift to Right 2 units
Vertical Stretch by 3
Vertical Shift up 5 units
What is the domain of
y=sqrt(-x+7)-3
Domain: (-∞, 7]
What is the range of
y= sqrt(-x+7)-3
Range: [-3, ∞)
Find the asymptotes of this function:
y=2/(x+1)+7
Vertical Asymptote: x=-1
Horizontal Asymptote: y=7
Oblique Asymptote: None
What is the inverse function of
y=6x^2-6
y=+- sqrt((x+6)/6)
Describe the transformation in words:
-sqrt(x+3)-5
Horizontal Shift left 3 units
Reflection over the X-axis
Vertical Shift down 5 units
Define
y=sqrt(25-x^2)
Give the domain of f.
Domain:
[-5, 5]
Define
y=sqrt(25-x^2)
Give the range of f.
Range:
[0, 5]
Find the Asymptotes of this function:
y=3/(x+2)
Vertical Asymptote: x=-2
Horizontal Asymptote: y=0
Oblique Asymptote: None
What is the inverse function of
y=(x+5)/(x-6)
y=(5+6x)/(x-1)