Algebra II Chapter 8 Test (A)
Show all your work for full credit.
Name___________________
Date___________________
Period__________________
For questions 1-4, let f ( x)  x 2  5 and g ( x)  x  7 . Perform each
function operation.
1) f ( x)  g ( x)
1)_________________(1)
2) ( f  g )( x)
2)_________________(2)
3) f ( x)  g ( x)
3)_________________(2)
g ( x)
4)
f ( x)
4)________________(1)
A new car that sells for $20,000 depreciates 15% each year.
5)Write a function that models the value of the car.
5)____________________(3)
6) Find the value of the car after 3 years.
6)______________(2)
For 7 and 8, let f ( x)  3 x  5 and g ( x)  x 2  1
7) find f  g (2)
7)______________(3)
8) find g ( f (1))
8)______________(3)
For the function f(x) = 2x + 4,
9) Graph f(x) (1 pt)
10) Find its inverse, f 1
11) Graph f 1 (1 pt)
12) Is f 1 a function?
10) f 1  _____________(2)
12) _________________(1)
For 13, identify whether the function represents exponential growth or
exponential decay
13) .05(1.09)
x
13)_____________(1)
14) Graph this function. Clearly label at least 3 points.
y  3(2) x
(4 pts)
For the following function, identify the parent function and what
transformations you would make to the parent function.
y  3 x  1
15) Parent function:_____________(1)
16)Transformations:______________
_________________________(2)
17) Horizontal asymptote of the transformed function: _______________(1)
18) If you invest $200 in a continuously compounded account at an interest
rate of 7%, how much will you have after 10 years?
18)_________________(3)
Write this equation in logarithmic form
19) 25  625
2
19)___________________(1)
Evaluate this logarithm
20) log 5 25
20)__________________(2)
21) Graph this logarithmic function. Clearly label at least 3 points.
y  log 5 ( x  3)
(4 pts)
Write this logarithmic function as a single logarithm.
22) 5 log 2 + 2 log 2
22)___________________(3)
Expand this logarithm.
y2
23) log
z
23)________________________(3)
Use the properties of logarithms to evaluate this expression.
24) log 8 4  log 8 16
24)___________________(3)
Solve each equation. Round to the nearest hundredth.
25) log( 7 x  3)  2
25)_________________(3)
26) 2 log x  log 5  2
26)________________(3)
 20
27)_________________(3)
27) 7
3x
28) ln x  ln 2  3
28)_________________(3)
Use the change of base formula to rewrite each expression using common
logarithms.
29) log 4 12
29)________________(1)
Extra credit (2 points):
A culture of 10 bacteria is started, and the number of bacteria will double
every hour. In about how many hours will there be 3,000,000 bacteria?
Extra credit (1 point):
Ellie lives on the nineteenth floor of an apartment building. Whenever she
gets into the elevator on the first floor, she presses the button for the fourth
floor, where she gets out and walks the rest of the way up. When she leaves
her apartment, however, she takes the elevator all the way down. Since she
would rather ride than walk, why does she do that?