Math 1090 Section 5 Review1
Read all directions carefully. This will be graded on completion, but you need to
show signicant work toward the solution of the problem.
1. Find all real solutions of the following absolute value equation.
j 2x + 3j = 1 + j x 5j
2. Find all real solutions of the following absolute value inequality.
j 4x 3j 3 j x + 1j
3. Graph the following equation and determine wheather it is a function of x, and
wheather or not it is one to one.
py + 9 = px
4. Find all solutions to the following equation
p
4x + 10 x 3 = 0
5. Find all solutions to the following equation.
p3
p
x + 2 + 3 3x 5 = 0
6. Find all solutions to the following equation.
5
3
4
x2+6x 7 x2+2x 35 = x2 6x+5
p p
7. If H (x) = x2 + 2x + 1 and G(x) = x 3 x nd and simplify (H G)(x) and
(G H )(x)
8. Find an inverse function for f (x) = x4 5 rst on the domain [0; 1) and then
on ( 1; 0]
9. Find the domain of Y (x) and nd Y ( 2) and Y (7) when
8 p2 5
>
< 3 x0
Y (x) = >
: +1 x < 0
x
x2
x
x
1
x
10. Using your knowledge of shifts, reections, and how graphs stretch, Graph
P (x) = 5 2j x 4j and write out and nd functions g(x); k(x); t(x); m(x),
and r(x) such that P (x) = (m g k r t)(x)
11. Say that in order to produce one box of corn akes, a companies overhead (xed
costs) is $5000 per month. If it costs $1 in variable costs to produce one box
and the boxes sell at a price of $1.50 each, how many boxes must be sold per
month in order for the company to turn a prot?
12. A company would like to have a revenue of $100,000 per month. If this company
sells bean bags for c dollars and the number of bean bags they sell is 1c 10 + c,
how many must they sell and what is the cost in order to reach their goal?
13. Find all real solutions of the following absolute value equation.
j 2x + 3j = 1 + j x 5j
14. Find all real solutions of the following absolute value inequality.
j 2x 1j 2 + j x + 1j
15. Graph the following equation and determine wheather it is a function of x, and
wheather or not it is one to one.
3y 2 = j x 1 j
16. Find all solutions to the following equation
p
p
16
x + 1 32 x + 1 20 = 0
17. Find all solutions to the following equation.
p 2
p
15
3x + 2 + 15 x 5 = 0
18. Find all solutions to the following equation.
x+1 + x 7 = 4x2 3x
x 2 x+2
x2 4
p
19. If M (x) = x 2 + x2 and L(x) = x 3 nd and simplify (L M )(x) and
(M L)(x)
20. Find an inverse function for P (x) = 3(x + 5)6 7 rst on the domain [ 5; 1)
and then on ( 1; 5]
21. Find the domain of I (x) and nd I ( 12 ) and I (2) when
8 3
< 3
I ( x) = :
(x 5)3
x4
x
x3
11 x 1
15 1 < x 0
22. Using your knowledge of shifts, reections, and how graphs stretch, Graph
h(x) = (x 2)3 +3, and write out and nd functions g(x); k(x); t(x), and r(x)
such that h(x) = (g k r t)(x).
F (x+h) F (x) ) for the function F (x) = x3 +
23. Find the dierence quotient (ie
h
2x + 1. Then simplify as much as possible and write as a function of x after
evaluating at h=0.
p
(10x+5)2 2
3
x
+2
5
1
24. Say that ( ) =
and
( ) =
nd all solu10
3
tions to G(x) = 1 and G(x) = 0.
Gx
G x