Here is what you need to know how to do for Exam 3 along
with corresponding practice problems in
the Chapter Reviews. You should also do the two practice exams I posted on my
web site and be
sure you can do the work in the 50 minute time period.
Section 3.1 linear function s and Their Properties
Problems Skill
1-6 Graph a linear function.
1-6 Find average rate of change ( slope ) of a linear function.
1-6 Determine whether a linear function is increasing, decreasing, or constant
35,36 Do word problems involving linear functions.
Section 3.2 We skipped this section
Section 3.3 Quadratic Functions and Their Properties
Axis of symmetry:
x =-b/2a
x-intercept ( value of x when y is 0) are solutions of 0 =
ax2
+ bx + c
y-intercept (value of y when x = 0) is c.
Problems Skill
9-14 Graph a quadratic function using transformations.
15-24 Find the vertex and axis of symmetry of a quadratic function.
15-24 Graph a quadratic function.
25-30 &
37-42 Find the local maximum or local minimum of a quadratic function.
Section 3.4 Quadratic Models & Building Quadratic Functions
Problems Skill
37-44 Solve word problems involving quadratic functions.
Section 3.5 Inequalities Involving Quadratic Functions
Problems Skill
31-34 Solve inequalities involving a quadratic function.
Section 4.1 Polynomial Functions and Models
Polynomial Function:
Power functions :
f (x) = xn, n ≥ 2 and even (pg 165)
looks like parabola with flattened nose and steeper sides.
f (x) = xn, n ≥ 3 and odd (pg 165)
looks like cubic with flattened middle and steeper sides.
Problems Skill
5-10 Graph polynomial functions using transformations.
11-18 Analyze the graph of a polynomial function
a. Find y-intercept (values of y when x = 0).
b. Find x-intercepts (values of x when y = 0) and their multiplicity. These are
the real zeros of the polynomial.
c. Determine whether the graph touches (even multiplicity) or crosses (odd
multiplicity)
x-axis at each x-intercept.
d. Determine end behavior (what does graph look like for large ± x):
 |
 |
 |
 |
Even multiplicity at x = 0
so graph TOUCHES |
Even multiplicity at x = 0
so graph TOUCHES |
Odd multiplicity at x = 0
so graph CROSSES |
Odd multiplicity at x = 0
so graph CROSSES |
 |
 |
 |
 |
e. Plot a couple of extra points and graph.
Section 4.2 Properties of Rational Functions
Rational Function:
R(x) =
p(x)/q(x)
where p and q are polynomials and q ≠ 0.
Vertical Asymptotes: With R reduced, if x = r makes q = 0
Hole: If R has a factor, x – a, that is common to p and q,
then there is a hole at x = a.
Horizontal Asymptote:
If [degree numerator] < [ degree denominator ]
then HA at y = 0
If [degree numerator] = [degree denominator]
then HA at y = L
If [degree numerator] = [degree denominator] + 1
then oblique asymptote at y = mx + b
If [degree numerator] > [degree denominator] +1
then no HA or OA
Problems Skill
19-22 For a rational function:
Find the domain (find values of x that make denominator 0).
Find the vertical asymptotes (find values of x IN THE REDUCED FRACTION that
make denominator 0).
Find horizontal or oblique asymptotes.
Section 4.3 Graph of a Rational Function
Problems Skill
23-34 Analyze the graph of a rational function
1. Factor, state domain, and THEN reduce.
2. Plot intercepts . For x-intercepts, state whether graph touches (multiplicity
is even) or
crosses (multiplicity is odd) x-axis.
3. Draw vertical asymptotes ( zeros of the denominator ).
4. Draw horizontal asymptotes:
If deg num < deg denom, y = 0 is a horizontal asymptote
If deg num = deg denom, y = L is a horizontal asymptote
If deg num = deg denom + 1, use long division to find oblique asymptote, y = mx
+ b
5. Plot where the graph crosses a horizontal or oblique asymptote, if it does.
That is,
solve the equation:
Function = asymptote
R(x) = y
6. If needed, plot a few extra points.
7. Connect the dots.
Section 4.4 Polynomial and Rational Inequalities
Problems Skill
35-36 Solve polynomial inequalities.
37-44 Solve rational inequalities.
1. Write inequality with 0 on one side .
2. Find real zeros of numerator and denominator.
3. Use real zeros to break up the number line into intervals.
4. Use a test point in each interval to see if the function is pos or neg.
