Advanced Functions Exam Review

Distributive Property

100

Rewrite using D.P.

4(x+2) = ?

4x+8

200

Rewrite using D.P.

-2(x²+2) = ?

-2x²-4

300

Rewrite using D.P.

-10[(1/2)x + 1/4] = ?

-5x-(5/2)

400

Foil. 

(8x+4)(2x+5) = ?

16x²+28x+20

500

Foil. 

(-12x²+4)(3x²-9) = ?

-36x⁴+120x²-36

Convert Exponential to Logarithms

100

Convert to Exponential. 

log₄16 = 2

4² = 16

200

Convert to Logarithms. 

3⁴ = y

log₃y = 4

300

Write the inverse of 

y = (2/3)^x

log_(2/3)y = x

400

Rewrite as Exponential and Evaluate. 

log₃(1/81) = x

x = -4

500

Rewrite as Exponential and Evaluate. 

log_(1/2)8 = x

x = -3

Solving Limits - Factoring

100

Factor and Evaluate. 

lim            (3x²+13x+4)/(2x²+5x-12)

x->-4

1

200

Factor and Evaluate. 

lim        (x²+6x+8)/(x+4)

x->2

4

300

Factor and Evaluate. 

lim  (x-1)/(x²+x-2)

x->1

1/3

400

Factor and Evaluate. 

lim      (x-4)/(x²-16)

x->4

1/8

500

Factor and Evaluate. 

lim       (x+4)/(x³+64)

x->-4

1/48

Inverse of Equations

100

Find the inverse of:

f(x) ={(-2,4), (7,5), (14,8)}

f^-1(x) = {(4,2), (5,7), (8,14)}

200

Find the inverse of:

f(x) = 2(x-3)

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

300

Find the inverse of:

Square root of (x+3) subtract 5

f^-1(x) = (x+5)²-3

400

Find the inverse of:

f(x) = [Square root of (4-x)/2] +3

f^-1(x) = 4-[2(x-3)]²

500

Find the inverse of:

f(x) = [4(x-13)⁷+4]/3

f^-1(x) = [seventh root (3x-4)/4]+13

Evaluate Logarithms Using Properties

100

Evaluate. 

log₄4

1

200

Evaluate. 

log1

0

300

Evaluate. 

log₃81

4

400

Evaluate. 

log₇49 + log₆1296

6

500

Evaluate. 

log13

1.114