INTERMEDIATE ALGEBRA STUDY GUIDE -- CH 9-10
9.1:
Ex:
Graph f(x) = 3x
Ex:
Graph y = 2–x
Ex: If
$2400 is deposited in an account paying 5% annual interest compounded quarterly,
how much will be in the account after 7 years?
Ex: If
$2400 is deposited in an account paying 5% annual interest compounded continuously,
how much will be in the account after 7 years?
9.2:
Ex: If
f(x) = x2 + 3x and g(x) = 5x, find
a. f(4)
b. g(s)
c. f(x+2) Clear
parentheses and collect like terms, if applicable
d. (g o f)(x) [Same as g(f(x))] Clear parentheses and collect like terms,
if applicable
Ex: Find the inverse of the function f(x) = 3x + 7
Ex:
Find the inverse of the function 
9.3:
Ex:
Write in log form: 53
= 125
Ex:
Write in exponential form: log3
81 = 4
Ex:
Graph y = log3 x
Ex:
Evaluate the following without a calculator:
a. log381
b. log(1000)
c. ln(e5)
d. log71
e. ln(e)
f. log2(2x)
g. log322
Ex: Use
the change of base theorem and a calculator to evaluate log421
9.4
Use properties of logarithms to expand the
expression: 
Use properties of logarithms to condense the
expression: 4 log2(x) – 3 log2(x+1)
+ 2 log2(x–4)
9.5
Ex:
Solve: 32x+3 = 92x
Ex:
Solve: log4(7x+1) =
log415
Ex: Solve for x:
log2 x = 5
Ex:
Solve for x: 2 log5 (x)
= 6
Ex:
Solve for x: logx 16 =
4
Ex:
Solve 34x+2 = 15
Ex:
Solve log4 x + log4
(x–6) = 2
9.6
Ex:
Use the exponential growth/decay model y = Cekt (or the continuous
compound interest model A = Pert) to find
a. How long will it take an investment to
double at a rate of 9% annual interest?
b. If the half-life of a radioactive
substance is 32 days, what is k?
10.1
Ex:
Write an equation of the circle with center (5,–3) and radius 6
Ex:
Give the center and radius of the circle, and sketch the graph:
x2
+ y2 = 8
(x–3)2
+ (y+2)2 = 16
x2
+ y2 + 4x – 12y + 15 = 0 Note: the coefficients of x and y will be even
integers.
Ex: From the graph, determine the center and radius, and use these to write the equation
Return to: Merced College; Don Power Updated 11/28/07 by Don Power