Combining Functions

Addition

100

f(x)= 8x + 5

g(x)= 7x + 2

Find (f+g)(x)

15x + 7

200

h(x)= -8x - 5

g(x)= x - 6

Find (h+g)(x)

-7x - 11

300

f(x)= 3x² - x + 3

g(x)= x² - 2

Find (f+g)(x)

4x² - x + 1

400

k(x)= -3x² - 9x + 3

c(x)= -5x² - 1 + 2x

Find (k+c)(x)

-8x² - 7x + 2

500

k(x)= x³ - 5 - x

c(x)= -5x² + 2x³

Find (k+c)(x)

3x³ - 5x² - x - 5

Subtraction

100

f(x)= 8x + 5

g(x)= 7x + 2

Find (f-g)(x)

x + 3

200

h(x)= -8x - 5

g(x)= x - 6

Find (h-g)(x)

-9x + 1

300

f(x)= 3x² - x + 3

g(x)= x² - 2

Find (f-g)(x)

2x² - x + 5

400

f(x)= 3x² - x + 3

g(x)= x² - 2

Find (g-f)(x)

-2x² + x - 5

500

k(x)= -3x² - 9x + 3

p(x)= -5x² - 1 + 2x

Find (p-k)(x)

-2x² + 11x - 4

Multiplication

100

f(x)= 6

h(x)= 8x

Find (f•h)(x)

48x

200

h(x)= 7

k(x)= -4x + 13

Find (h•k)(x)

-28x + 91

300

d(x)= 3x

g(x)= x + 36

Find (d•g)(x)

3x² + 108x

400

f(x)= x + 5

g(x)= x + 2

Find (f•g)(x)

x² + 7x + 10

500

f(x)= 2x - 5

g(x)= 2x + 3

Find (f•g)(x)

4x² - 4x - 15

Division

100

f(x)= 7

h(x)= 8x

Find (f÷h)(x)

7 / 8x

200

g(x)= 3x + 7

f(x)= 5x - 8

Find (g÷f)(x)

(3x + 7)  /  (5x - 8)

400

p(x)= 6x + 18

c(x)= 3

Find (p÷c)(x)

2x + 6

Sequences

100

88, 109, 130,...

Find the next 2 terms.

Find term 20 using the explicit formula.

151, 172

a₂₀ = 88+21(20-1) = 487

300

4, 8, 16,...

Find the next term.

Find term 8 by using the explicit formula.

32

a₈=4(2)^8-1 = 512

500

-24786, 8262, -2754,...

Find the next term.

Find term 7 by using the explicit formula.

918

a₇=-24786(-1/3)^7-1  = -34