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Math 253 Chapters 7-8 Review

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:

#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

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