Math Final Project

Inverse

100

Find the inverse

f(x)=3x+2

f^-1(x)= (x-2)/3

200

Find the inverse

f(x)=x³-2

f^-1(x)=^3 square root x+2

300

Find the inverse

f(x)=(1/2)^x+6

f^-1(x)= -log₂ (x-6)

400

Find the inverse

y=log₃(8x)

y=(1/8)3^x

500

Inverse the ordered pairs

f=(-1,-1),(8,8),(2,5),(5,2)

f^-1= (-1,-1),(8,8),(5,2),(2,5)

Patterns

100

Find the common ration of this geometric sequence

1,-2,4,-8

common ratio is 2

200

Find the common difference in the arithmetic sequence

-6,3,12,21

common difference is 9

300

Predict the next 3 numbers in the pattern

11,13,15,17,19,?,?,?

21,23,25

400

Find the mean

26,14,23,35,52,36,42,68,49,32,50,56,68,43

mean=42.4

500

Write in standard form

5w-w⁶+0.4w³-10.5

-w⁶+0.4w³+5w-10.5

Equations

100

x²-6x+9=0

x=3

200

Find the solutions

y=x²+2x+9

y=-x+7

y¹=(-2,9)

y²=(-1,8)

300

Solve for x

5/(x+3)  -  1/(x+5)  =  1/(x²+8x+15)

x= - 23/4

400

Factor the expression

3x²-3x-60

3(x+4)(x-5)

500

Multiply 

(7-9i)(7+9i)

130

Logs

100

How much does 'e' equal in a logarithm equation

2.718

200

Expand the logarithm

log₅ (2/3)

log₅ 2- log₅ 3

300

Expand the expression

ln(7x²)

ln7+ 2ln(x)

400

Change of Base Formula 

ln21

log21/loge

ln21=3.045

500

Write in logarithmic form

y=17^x

log₁₇ y=x