Semester 2 Algebra 2 Study Game

function operation

100

f(x)=x+2, g(x)=x+5

 (f+g)(x)

2x+7

200

f(x)=2x, g(x)=x−3

 (f−g)(x)

x+3

300

f(x)=x+1, g(x)=x+4  

(fg)(x)

(x+1)(x+4)

400

f(x)=x+2, g(x)=x−1 

(f/g)(x)

 (x+2)/(x−1)

500

f(x)=2x+1, g(x)=x+3

(f+g)(x)

3x+4

function composition

100

f(x)=x+2, g(x)=x+3 

f(g(x))

x+5

200

f(x)=2x, g(x)=x+1 

f(g(x))

2x+2

300

f(x)=x², g(x)=x−2 

f(g(x))

(x−2)^

400

f(x)=x+3, g(x)=2x 

g(f(x))

2x+6

500

f(x)=3x, g(x)=x−4 

f(g(x))

3x−12

inverse functions

100

Find inverse: f(x)=x+5

 f⁻¹(x)=x−5

200

Find inverse: f(x)=2x

 f⁻¹(x)=x/2

300

Find inverse: f(x)=(x−3)/4

f⁻¹(x)=4x+3

400

Are they inverses? f(x)=2x+1, g(x)=(x−1)/2

Yes

500

Find inverse: f(x)=3x−6

f⁻¹(x)=(x+6)/3

logarithms

100

Rewrite: 2³ = 8

log₂(8) = 3

200

Rewrite: log₃(9) = 2

 3² = 9

300

Solve: log(x) = 2

x = 100

400

Solve: log₄(x) = 3

x = 64

500

Solve: log₂(32) = x

x = 5

exponential equations

100

 2^x = 8

x = 3

200

3^(x+1) = 27

x = 2

300

2^(x+2) = 32

x = 3

400

2^x = 10

x = 3.3

500

4^(x−1) = 64

x = 4