Math 2
Test Review
Name ______________________________________________________
Date _______________________________________________________
Remember your test will be administered in two sections… Calculator and Non-Calculator.
(1) I would advise you to memorize these graphs to help you visualize a graph based off a given equation.
Exponential Growth
Equation:
Exponential Decay
Equation:
Reflected Expo. Growth
Equation:
Reflected Expo. Decay
Equation:
Asymptote:
Asymptote:
Asymptote:
Asymptote:
y-intercept:
y-intercept:
y-intercept:
y-intercept:
Range:
Range:
Range:
Range:
End Behavior:
x →∞, y→
x → -∞, y→
End Behavior:
x →∞, y→
x → -∞, y→
End Behavior:
x →∞, y→
x → -∞, y→
End Behavior:
x →∞, y→
x → -∞, y→
Now, if you can first classify the following equations as one of the four above “parent functions”… The rest will be a lot
easier!!!
(2) Given the exponential function g (x )   12   3 , find all of the following
Asymptote
y-intercept
Domain (interval notation)
Range (interval notation)
Growth/Decay
Interval of inc/dec
Domain (set builder notation)
Range (set builder notation)
End behavior
Transformations
AROC over interval 3  x  1
Range (words)
x
(2) Given the exponential function g (x )  3 x 1 , find all of the following
Asymptote
y-intercept
Domain (interval notation)
Range (interval notation)
Growth/Decay
Interval of inc/dec
Domain (set builder notation)
Range (set builder notation)
End behavior
Transformations
AROC over interval 0  x  2
Range (words)
 5 x 4 
(3) 
3 
 15y 
3

(4) 4 x 8 y 3 3 x 2y 4

2
(5)
3m 7
m9
 12 x 4 y 2 
(6) 
8 6 
 36 x y 
2
(7)
 9x
4
y 3    x 5y 3 
2
2
(8)
 5x
4
y 2z 3 
3
 Application problems: You need to know the formulas y = abx and A(t) = P(1 + nr )nt.
(9) The population of a small city is 1,849 in 1998 but grew at a steady rate of 2.5% per month. What was the population
in 2006?
(10) The value of a car depreciates at a rate of 9% per year. If the car was worth $18,390 eight years ago, how much is it
worth now?
(11) A petri dish contained 189 bacteria at noon and triples every 30 minutes. How many bacteria will there be at 2pm?
___________ How many will there be at 3:15? ___________________________ How many were there at 11am?
__________
(12) John deposited $1,240 into an account which compounded semiannually at a rate of 7.9%. If he leaves his money in
the account for 8 years, how much money will he have?

(13) 2
Solving Equations and Inequalities.
2 x 8
8
2 x 12
(14) 32 2 x  6  16 2 x
(15)
 181
x 2
 3 2 x 4
Geometric Sequence. You need to know the explicit formula: tn = t1(r)n – 1
(16) Determine if the following are geometric or arithmetic sequences and state the common ratio/difference.
a. -12, 9,  27 4 …
b. 20, 18, 16, 14…
c. 2 3 , 2, 6,
18…

(17) Given a geometric sequence 4, 12, 36, 108…, find all of the following:
a. The common ratio: _________________
b. The explicit formula: _____________________
_______________
c. t10 =