Transformations and Combinations

Transformations

100

Transformations on the function f(x) + 6

up 6

200

Transformations on 3f(x - 4)

right 4, vertical stretch

300

Transformations on -f(3x) - 2

horizontal compression, reflect over x, down 2

Add/Subtract Functions

100

(f+g)(x) if f(x) = x² and g(x) = 4x - 5

x² + 4x -5

200

(f - g)(x) if f(x) = x² and g(x) = 4x - 5

x² - 4x + 5

300

(f + g)(x) if f(x) = 2x - 5 and g(x) = 2 - x

x - 3

Multiply Functions

100

(fg)(x) if f(x) = 2x - 5 and g(x) = 2 - x

-2x² +9x -10

200

(fg)(x) if f(x) = x² and g(x) = 4x - 5

4x³ -5x²

300

(fg)(x) if f(x) = x² + 6 and g(x) = sqrt(1-x)

(x² + 6)*sqrt(1-x)

Divide Functions

100

(f/g)(x) if f(x) = 2x - 5 and g(x) = 2 - x

(2x - 5)/(2 - x)

200

(f/g)(x) if f(x) = x² and g(x) = 4x - 5

x²/(4x - 5)

300

(f/g)(x) if f(x) = x² + 6 and g(x) = sqrt(1-x)

SIMPLIFY ALL THE WAY

((x2 + 6)*sqrt(1-x))/(1-x)

Composition of Functions

100

g o f if f(x) = x² and g(x) = x - 1

What is x² - 1

g o f = g(f(x)) = g(x²) = x² - 1

200

f o g if f(x) = x² and g(x) = x - 1

What is x² - 2x + 2?

f o g = f(g(x)) = f(x - 1) = (x-1)² = x² - 2x + 2

300

g o g if g(x) = x³ + 1

x⁹ + 3x⁶ + 3x³ + 2