MATH 107 UMGC Algebraic Functions Quiz

University of Maryland University CollegeMath 107 – College Algebra
Quiz 5
Free Response, Multiple Choice, and Yes/No Problems, 6 Points Each.
You may write answers after problems (you may use Microsoft Equation). If you prefer
handwriting, prepare you answer sheet, scan it, and prepare a file in PDF format.
Write an exact answers, using fractions or radicals as needed. Simplify answers if possible.
1. Given that f(x) = 55x + 22 and g(x) = x3, find (f ◦ g)(− 3).
2. Find (f ◦ g)(x) and (g ◦ f)(x) for f ( x) = 5 x − 4, g ( x) =
x+4
.
5
3. Find ( f g )( x) and ( g f )( x) and the domain of each.
f ( x) = 2 x + 1, g ( x) = x .
4. Choose the graph that shows a graph of a one-to-one function and its inverse (shown red and
dashed).
A
C
B
D
5. Determine whether the function f ( x) = x + 2 is one-to-one.
Yes
6. Find the inverse of the function f ( x) = −
No
3
.
x +1
2
In problems 7-8, solve radical equations.
7. x + 1 + 1 = x
8.
6x + 7 = x + 2
x
1
9. Choose the correct graph for the function y =   .
2
A
B
C
D
10. Choose the correct graph for the function f ( x) = −0.35e− x + 3 .
A
B
11. Find the domain of the function H ( x) = log 7 x9 .
A. All positive real numbers.
B. All nonzero real numbers.
C. All real numbers except 7.
D. All real numbers.
12. Find the logarithm.
log 5 54
C
D
3
13. Find the logarithm.
log10−8
14. Choose the correct graph for the function y = log8 x
A
B
C
D
15. Choose the correct graph. f ( x) = 3x is in the solid red line. f −1 ( x) = log 3 x is the dashed blue
line.
A
B
16. For the function f ( x) = log3 ( x + 1) find:
(a) The domain in interval notation
(b) The vertical asymptote
C
D