Functions and Composite Functions

Linear Functions

100

f(x) = x + 2 

f(4) =

(f4) = 6

200

f(x) = x + 2 

f(-2) =

f(-2) = 0

300

g(x) = 2 - x

g(5) = 

g(5) = -3

400

f(x) = 3x - 9

f(4) = 

f(4) = 3

500

b(x) = 3x - 15

b(7) = 

b(7) = 6

Quadratic Functions

100

h(x) = x² - 2x

h(5) = 

h(5) = 15

200

d(x) = x² +3

d(-10) =

d(-10) = 103

300

a(x) = 3x² - x

a(2) =

a(2) = 10

400

h(x) = x² - 9

h(-3) =

h(-3) = 0

500

f(x) = 100/x² 

f(10) =

f(10) = 1

Combined Functions

100

t(x) = x²

s(x) = 3x

What is (s/t)(3))?

(s/t)(3)) = 1

200

g(x) = 2^x

f(x) = x + 2

What is (g*f)(1))?

(g*f)(1)) = 6

300

d(x) = x + 5

e(x) = 3x

What is (d+e)(5)?

(d+e)(5) = 25

400

g(x) = x-1

b(x) = x+1

What is g(b(x))?

g(b(x)) = x

500

d(x) = 8 - 4x

k(x) = 2x + 5

What is (d*k)(x)?

(d*k)(x) = -8x² -4x +40

Composite Functions

100

a(x) = |-3x|

g(x) = x - 6

What is a(g(-3))?

a(g(-3)) = 27

200

a(x) = |-3x|

g(x) = 2^x

What is a(g(2))? 

a(g(2)) = 12

300

f(x) = -3x - 15

h(x) = 6 - 3x

What is a(g(-3))?

a(-3) = -60

400

j(x) = x^2 - 5

k(x) = 5 + x

What is j(k(-5))?

j(k(-5)) = -5

500

b(x) = 5 - x 

a(x) = 3

What is b(a(-3))?

b(a(-3)) = 2

Mixed Bag

100

b(x) = 6x - 5

What is b(10)?

b(10) = 55

200

b(x) = x^2

f(x) = x + 2

b(f(2)) = 

b(f(2)) = 16

300

b(x) = 9

a(x) = 3x

What is a(b(2))? 

a(b(2)) = 27

400

b(x) = x^2 + 4

What is b(5)?

b(5) = 29

500

b(x) = x+5

h(x) = x² - 2x

What is (b+h)(3)?

(b+h)(3) = 11