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Transformation to Equation

100

Reciprocal

f(x) = 1/x

200

Cube Root

Down 7

f(x) = (x)³ - 7

300

Absolute Value

Right 3

Up 5

f(x) = |x-3| + 5

400

Square Root

Reflect over x-axis

Down 2

f(x) = - √x - 2

500

Quadratic

Left 8

Up 5

f(x) = (x+8)² + 5

Composition

100

f(t) = 2t + 5 

g(t) = t³ - 2t² 

f(g(0))

 

5

200

g(a) = 4a 

f(a) = 4a - 4 

g(f(3))

32

300

h(a) = 2a + 3 

g(a) = a² + 2a 

h(g(1))

9

400

h(n) = 2n + 2 

g(n) = 2n 

h(g(n)) 

4n + 2

500

g(n) = -4n - 4 

h(n) = n² + 5 + n 

g(h(n))

-4n² - 4n - 24

List the Transformations

100

g(x) = x² - 1

down 1

200

f(x) = |x-1| + 3

right 1

up 3

300

h(x) = (x-2)³ + 4

right 2

up 4

400

g(x) = -(x+1)² + 3

left 1

flip over x-axis

up 3

500

f(x) = -|x+5| - 2

left 5

flip over x-axis

down 2

Function Arithmetic

100

g(a) = 2a − 1

h(a) = 3a − 3

(gh)(−4)

135

200

h(x) = 3x + 3

g(x) = −4x + 1

(h + g)(10)

-6

300

f (x) = 4x − 3

g(x) = x³ + 2x

(f − g)(4)

-59

400

g(a) = 3a + 2

f (a) = 2a − 4

(g/f)(3)

11/2

500

h(t) = 2t + 1

g(t) = 2t + 2

(h − g)(t)

-1

Misc.

100

Square Root

f(x) = √x

200

h(x) = -x² + 1

flip over x-axis

up 1

300

h(x) = |-x-2| + 1

left 2

flip over y-axis

up 1

400

f(n) = -4n + 1

g(n) = -2n - 5

f(g(n))

8n + 21

500

g(x) = −x² − 1 − 2x

f(x) = x + 5

(g − f )(x)

-x² - 3x - 6