Transformations
Describe the transformations of the following function in reference to the parent function.
f(x) = 1/2abs(x)-3
vertical shrink by a factor of 1/2, vertical translation down 3
Solve for x.
6 + abs(9 + x) = 22
x = 7, -25
These are the steps for algebraically calculating a functions inverse.
1. Switch x & y variables
2. Solve for y (or dependent variable)
3. Label with proper inverse notation
Given f(x) = 2x-5 & g(x) = 3x+7
find f(g(x))
f(g(x)) = 6x + 9
Given: f(x) = 2x+1 g(x) = -3x+5 and h(x) = 7x
Find (f+h)(x)
(f+h)(x) = 9x+1
Describe the transformations of the function below, f(x), in reference to the parent function, p(x)
p(x) = absx, f(x) = -3/2abs(x + 6)+2
-reflection over the x-axis
-vertical stretch by a factor of 3/2
-horizontal translation left 6
-vertical translation up 2
Solve for x.
2abs(x - 4) + 3 = -19
no solution
Given f(x), find f^-1(x)
f(x) = 2x - 5
f^-1(x) = (x + 5)/2
Given f(x) = 2x-5 & g(x) = 3x+7
find f(g(3))
f(g(3)) = 27
Given: f(x) = 2x+1 g(x) = -3x+5 and h(x) = 7x
Find (f-g)(x)
(f-g)(x) = 5x-4
Create a new function, k(x), that transformations the absolute value parent function, p(x), in the follow ways:
-reflection over the x-axis
-vertical stretch by a factor of 2
-horizontal translation right 3
k(x) = -2abs(x - 3)
Solve for x. Write your answer in inequality notation.
-8abs(x - 10) < -112
x < -4 or x > 24
This is the way to graphically determine if two functions are inverses.
1. There is symmetry across y = x
2. The domain & range switch
Find r(q(-2)) given:
q(x) = 1/2(x - 4)
r(x) = 3x + 10
r(q(-2)) = 1
Given: f(x) = 2x+1 g(x) = -3x+5 and h(x) = 7x
Find (h*g)(x)
(h*g)(x) = -21x^2+35x
Describe the transformations of the function below, h(x), that transform the parent function, f(x)
h(x) = -3f(x-2)
-vertical stretch by a factor of 3
-reflection over the x-axis
-horizontal translation right 2
Solve for x.
4abs(7x + 1) + 5 = 9
x = 0, -2/7
This is the way to algebraically determine if two functions are inverses.
f(f^-1(x)) = x & f^-1(f(x)) = x
Find q(r(x)) given:
q(x) = 1/2(x - 4)
r(x) = 3x + 10
q(r(x)) = 3/2x + 1
Given: f(x) = 2x+1 g(x) = -3x+5 and h(x) = 7x
Find (f/g)(x)
(f/g)(x)=(2x+1)/(-3x+5); xne5/3
Describe the transformations of the functions:
f(x) = -5/4f(x + 3) - 5
-vertical stretch by a factor of 5/4
-reflection over the x-axis
-horizontal translation left 3
-vertical translation down 5
Solve for x. Write you answer in interval notation
abs(x + 5)/2<= 2
Hint: Graph the solutions on a number line then write the interval notation.
[-9, -1]
Given f(x), find f^-1(x)
f(x) = (2x - 3)/7
f^-1(x) = (7x + 3)/2
Given: f(x) = 5x - 7
Find f(f(x))
f(f(x)) = 25x - 42
Given: f(x) = 2x+1 g(x) = -3x+5 and h(x) = 7x
Find (f*g)(3)
(f*g)(3)=-28