composition of functions
inverse of functions
transformation of functions
Even/Odd
100

f(x) = 3x + 4 

g(x) = x - 2 

Find f(g(2))

 f(g(2)) = 4

100

Find the inverse of the function 

f(x) = -4x + 1 

f-1(x) = x - 1 / -4 

or 

f-(x) = -1/4 x + 1/4 


100

Describe the transformation: 

f(x) = x3

g(x) = 3 (x + 1)3

-shift one unit to the left 

-Vertical translation of a factor of 3 

100

Is the function even, odd, or neither?

y=x^2

Even

200

f(x) = x + 3 

g(x) = x2 - 4x 

Find g(f(3)) 


g(f(3)) = 12

200

Find the inverse of

f(x) = x + 3  

f-1(x) = x - 3 

200

Describe the transformation: 

g(x) = x2

f(x) = (x - 3)2 + 4 

-Shifts 3 units right 

-Shifts 4 units up 


200

Is the function even, odd, or neither?

y=2x+7

Neither

300

h(x) = 4x - 12 

f(x) = 6x2 +2 

Find f(h(4)) 

f(h(x)) = 98 

300

Find the inverse function of

f(x) = (7x + 18) / 2

f-1(x) = (2x - 18) / 7 

300

Write the new equation for the transformation: 

f(x) = x2

-translates up 1 unit 

-translates left 3 units 

- expands vertically by a factor of 3 

g(x) = 3(x+3)2 +1 

300

Is the function even, odd, or neither?

y=x^3-3x

Odd

400

f(x) = x + 4 

g(x) = x2 - 6x

Find f(g(x)) 

f(g(x)) = x2 -6x +4 

400

find the inverse of 

g(x) = - x + 3 

g-1(x) = -x + 3 

400

Write a transformed equation for the following 

f(x) = x3

-expanded vertically by a factor of 4

-reflect across the x-axis

-translate left 2 units

-translate up 3 units

g(x) = -4(x + 2)3 + 3

400

f(x)=-2x+3

Neither

500

f(x) = 6x - 2 

g(x) = x2 + 5x - 4 

Find g(f(x)) 

g(f(x)) = 36x2 - 19x

500

Find the inverse of 

h(x) = 3 x3 - 3 

h-1(x) = cube root of ((x + 3)/ 3) 

500

Write a transformed equation for the following 

f(x) = x

-compress vertically by a factor of 1/3

-reflect across the x-axis

-translate right 2 units

-translate down 3 units

g(x) = -1/3(x - 2) -3

500

Is the function even, odd, or neither?

y=4x-2x^3+3

Neither; f(1)=5, f(-1)=1

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