Review for Chapter 4 Test
TRY TO DO AS MUCH OF THIS STUDY GUIDE AS POSSILE WITHOUT A CALCULATOR.
Your test will have a calculator portion and a non-calculator portion, and the more you are able to do
without a calculator, the better off you will be!
1. a) Using the Rational Root Theorem, list the possible roots of the function f ( x)  2 x3  3x  5
b) Now, using synthetic OR the remainder theorem, decide which is an actual root. (Remember: If you get
a zero at the end of either, that is the root!)
c) Using the root you found, factor f(x) into two factors.
2. Write an equation for a quintic polynomial that goes through the point (3, 60) with zeros 1, -1, 2, -7, & 0.
Sketch an accurate graph.
Plot the zeros and the given point.
Describe the end behavior.
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3. Find a quartic equation that goes through the points (0, 1) and (0, -3) and bounces at 0.
4. a) Write each of the following in the form f(x) = Axk
b) Sketch each using your guide.
c) State the domain of each function.
𝑓(𝑥) =
1 4
2𝑥 5 +6𝑥 3
𝑓(𝑥) =
3𝑥 2 +9
1
5
√𝑥 3
𝑓(𝑥) =
𝑥5𝑥3
5. Factor f ( x)  2 x 4  3x 2  x , knowing that 1 is a zero.
To start, use synthetic or long division to divide
6. Where is f ( x)   x  3
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53
1
(8𝑥 4 )3
2 x 4  3x 2  x
x 1
not differentiable? Use your rules to sketch a quick graph first.
7. Use the function 𝑓(𝑥) =
𝑥 3 +2𝑥 2 −16𝑥−32
𝑥 2 −3𝑥−4
to answer the following.
a. Factor the top and the bottom completely
b. x-intercepts:
c. y-intercetps:
d. vertical asymptotes:
e. holes:
f. end behavior asymptote:
g. describe the end behavior in limit notation
8. Use the roots to give a possible equation for each function shown.
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9. Match each of the graphs to its equation.
1
f(x) = −𝑥 6 ____
a.
b.
c.
e.
f.
5
f(x) = 𝑥 3 ____
3
f(x) = 𝑥 5 ____
1
f(x) = 𝑥 −2 ____
d.
3
f(x) = 𝑥 2 ____
f(x) = 𝑥 −5 ____
10. Match each of the graphs to its equation.
a.
b.
f(x) = x + 5x – 4x – 20 ____
3
2
f(x) = -x2 – 3x + 4 ____
f(x) = x3(x – 2)4(x + 1)2(x – 1) ____
c.
d.
f(x) = x3 + 5x2 + 4x + 20 ____
f(x) = (x – 1)(x + 2)(x – 3) ____
f(x) = x3(x + 1)2(x – 2)4(x – 1) ____
e.
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f.
11. Match each of the graphs to its equation.
f(x) =
𝑥 2 −1
𝑥 2 +2𝑥−3
____
a.
b.
.
f(x) =
f(x) =
f(x) =
1
𝑥^5
+2
____
𝑥 4 −𝑥 3 −2𝑥 2 +2𝑥
𝑥 2 −1
𝑥 3 −𝑥
𝑥 2 +2𝑥−3
____
____
d.
c.
f(x) =
𝑥 2 +4
1−𝑥
____
e.
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