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Review of Prerequisite Skills
There are many features that we can analyze to help us sketch the graph of a
function. For example, we can try to determine the x- and y-intercepts of the
graph, we can test for horizontal and vertical asymptotes using limits, and we can
use our knowledge of certain kinds of functions to help us determine domains,
ranges, and possible symmetries.
In this chapter, we will use the derivatives of functions, in conjunction with the
features mentioned above, to analyze functions and their graphs. Before you
begin, you should
• be able to solve simple equations and inequalities
• know how to sketch graphs of parent functions and simple transformations of
these graphs (including quadratic, cubic, and root functions)
• understand the intuitive concept of a limit of a function and be able to evaluate
simple limits
• be able to determine the derivatives of functions using all known rules
Exercise
1. Solve each equation.
a. 2y 2 y 3 0
c. 4x 2 20x 25 0
b. x 2 5x 3 17
d. y 3 4y 2 y 6 0
2. Solve each inequality.
a. 3x 9 6 2
c. t 2 2t 6 3
b. 513 x2 3x 1
d. x 2 3x 4 7 0
3. Sketch the graph of each function.
a. f 1x2 1x 12 2 3
c.
f 1x2 2x 4
x 2
b. f 1x2 x 2 5x 6
d. f 1x2 x 2
4. Evaluate each limit.
a. lim
xS2 1x2 42
c.
x 3 27
lim
xS3 x 3
b. lim x 2 3x 10
xS2 x 2
d. lim xS4
162 REVIEW OF PREREQUISITE SKILLS
NEL