Exam #2 Practice Problems Math 115: Precalculus July 20, 2009
Exam #2 will be on Wednesday, July 22nd at 1:00pm. It will cover sections 1.7, 2.1, 2.2,
2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, and 3.6 of Dugopolskiโs Precalculus textbook, as well as
material about concavity of functions that we covered in class. Look over the following prob-
lems and review previously assigned homework, quizzes, and handouts to be fully prepared
for the exam.
1. Solve the following linear, compound, and quadratic inequalities. Write your final
answers in interval notation.
(a) โ2(3xโ2) โฅ4โx(b) 5 โx < 4 and 1
2xโ5<1 (c) 1 <3xโ5โค7
(d) t2+ 9 >0 (e) x2โ4xโฅ12 (f) โ3z2โ5>2z
2. Determine whether the following relations and graphs represent yas a function of x.
(a) {(5,7),(0,7),(1,7),(9,7)}(b) {(2,6),(3,5),(2,7)}(c) {(โ1,1),(2,2),(3,3)}
(d) (e)
3. Solve the following problems involving average rates of change. Give correct units.
(a) If a new Mustang is valued at $16,000 and give years later it is valued at $4,000, then
what is the average rate of change of its value during those five years?
(b) Billy Joe McCallister jumped off the Tallahatchie Bridge, 70 ft above the water, with
a bungie cord tied to his legs. If he was 6 ft above the water 2 seconds after jumping, then
what was the average rate of change of his altitude as the time varied from 0 to 2 seconds?
4. Compute and simplify the difference quotient for the following functions.
(a) f(x) = x2โx+ 3 (b) g(x) = 4 (c) f(x) = 2
x
5. Graph the following functions.
(a) f(x) = โโ25 โx2+ 2 (b) g(x) = โ|x+ 1|(c) h(x) = 2 โโx
(d) f(x) = 3|xโ2|+ 1 (e) g(x) = โโxโ3 + 1 (f) h(x) = โ(x+ 2)3โ1
