**DIRECTIONS:** Show all work neatly and clearly and
thoroughly. Assume all variables represent real

numbers greater than or equal to zero. Except for graphs, enclose answers in**
boxes.**

#1 – 4: Rewrite as exponential expressions.

#5 –8: Rewrite as radical expressions.

#9 – 14: Simplify.

#15 – 25: Simplify.

#26 – 27: Solve.

#28 – 36: Simplify.

37. For the function ,
state the domain in both set-builder notation and interval

notation. Make a table of values for f , and sketch the graph of the function.

Domain (using set-builder notation):

Domain (using interval notation):

38. Solve by factoring:

39. Solve by completing the square:

40. Solve by using the quadratic formula:

#41 - 47: Solve.

#48 – 49: Write a quadratic equation that has integer
coefficients and has as solutions the given pair of

numbers.

#50 – 52: Use the discriminant to determine whether the
quadratic equation has one real number

solution, two real number solutions, or two complex number solutions.

#53 – 57: For each problem, do the following: (A) graph
the solution to the inequality (remember to

label important coordinates **underneath** the number line), (B) write the
solution using interval

notation, and (C) write the solution using set-builder notation.

(A) Number line (label important coordinates):

(B) Solution using interval notation:

(C) Solution using set-builder notation:

(A) Number line (label important coordinates):

(B) Solution using interval notation:

(C) Solution using set-builder notation:

(A) Number line (label important coordinates):

(B) Solution using interval notation:

(C) Solution using set-builder notation:

(B) Solution using interval notation:

(C) Solution using set-builder notation:

(B) Solution using interval notation:

(C) Solution using set-builder notation:

#58 – 61: Solve.

62. A 15-foot ladder is leaning against a building. How
high will the ladder reach when the bottom of

the ladder is 5 feet from the building. [Give an exact answer; then round your
answer to the nearest

tenth of a foot.]

63. It takes 6 hours longer for a small air conditioner to
cool a storage room than it does for a larger air

conditioner. If they work together, the room can be cooled in 2 hours. How long
would it take the

smaller air conditioner to cool the room if it worked alone? [Give an exact
answer; then round your

answer to the nearest tenth of an hour.]

64. A manufacturer of mountain bikes believes that the
revenue R , in dollars, that the company

receives is related to the price x , in dollars, of a bike by the function

.

What price will give the maximum revenue? What will the maximum revenue be?

65. Given, find: (A)
the vertex, (B) the axis of symmetry, (C) the rule for

f in standard form, (D) the x - intercepts ,
(E) the y - intercept ,

(F) the domain, (G) the range, (H) sketch the graph, (I) state which f has, a
maximum or a

minimum, and state the value of x where the maximum or minimum occurs.

(A) Vertex= ( , )

(B) Axis of Symmetry:

(C):

(D) x - intercepts :

(E) y - intercept :

(F) Domain:

(G) Range:

66. Use the discriminant to determine the number of x - intercepts for