Download Review: Solving Equations and Inequalities

Name:
Date:
Algebra 2
Review Problems
Review: Solving Equations and Inequalities
Types of problems:
Methods you’ll need to use:
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solving an equation
finding a function’s zeros
solving an inequality that has a number on one side
(such as f(x) ≤ #)
solving a double inequality (such as # ≤ f(x) ≤ #)
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algebraic solving (when the functions
involved are linear)
graphical solving using intersections
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graphical solving using zeros
1. A graph of a function f(x) is given. Answer these
questions about f(x). If an answer involves a
non-whole number, make a reasonable estimate.
The whole graph is shown. No arrows at ends!
a. What is the domain of f(x)?
b. Solve f(x) = 1.
c. Find the zeros of f(x).
d. Solve -4 < f(x) < –2.
e. Solve f x   0
2. Answer the following questions involving function f(x) =  12 ( x  4)  3 . This is a line, so add
arrows to the end!
graph of f(x) =  12 ( x  4)  3
a. Solve graphically:  1 ( x  4)  3   1 .
2
b. Solve graphically:  12 ( x  4)  3   1 .
c. Solve graphically:  1   12 ( x  4)  3  2 .
d. Find the zeros of f(x) =  12 ( x  4)  3
graphically.
Name:
Date:
Algebra 2
Review Problems
3. g(x) is below. Questions may require estimating. g(x) continues down on both sides.
a. Find the domain of g(x) .
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b. Find the range of g(x) .
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c. Find the zero(s) of g(x) .
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d. Find g(2) .
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e. Solve g(x)  4 .
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f. Solve g(x)  2 .
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g. Solve g(x)  4
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h. Solve the equation g(x)  7 .
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4. Answer the following questions about the function f (x) given at the right. You may assume
that the graphcontinues infinitely far in both directions.
a. Find the domain of f(x).
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b. Find the range of f(x).
c. Find the zero of f(x).
d. Solve f(x) = –4.
e. Solve f(x) ≥ –2.
f. Solve f(x) < 2.
g. Solve 0 < f(x) < 2.
Name:
Date:
Algebra 2
Review Problems
5. a. Solve graphically on your calculator: 3x + 1 = –x + 5. (Use INTERSECTIONS.)
b. Check your answers to part a by solving the same problems algebraically.
3x + 1 = –x + 5
6. a. Solve graphically on your calculator using INTERSECTIONS:  4  2x  2  6 .
(Draw the calculator graph that you use.) Note that you will need two horizontal lines.
b. Solve algebraically:  4  2x  2  6 .
Name:
Date:
7.
Algebra 2
Review Problems
Solve graphically on your calculator by finding a zero. (Hint: you will need to get 0 on
one side of = first)
(Draw the calculator graph you used.)
0.7x + 3 > 3.2x – 5.5
8. Solve algebraically:
a. –4 < – 13 x + 2 < 7
b. 4 ≤ –2(x + 3) + 1 ≤ 13
Name:
Date:
Algebra 2
Review Problems
ANSWERS:
1. a. –5 ≤ x ≤ 6
b. x = 0, x ≈ 2.6, x ≈ 5.4
c. x = –1, x = 3, x = 5.
d. –5 ≤ x ≤ 3.
e. –1 < x < 3, 5 < x ≤ 6.
2. a. x = 4
b. x < 4
c. –2 < x < 4 d. x = 2
3. a. All real numbers b. gx  4.2
c. x = 1.5, x = –2.5
f. x  2 or x  1 g.  1  x  0
4. a/b All real numbers c. x  2
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d. 2
e. –1, 0
h. No solution
d. x  4
e. x  1
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5.
a. x = 1
b. x = 1
6.
a/b. –4 ≤ x ≤ 1.
7. a. –2.5x + 8.5 > 0
b.
8. a.  15  x  18
b.  9  x  4.5
x = 3.4
f. x  5
g. –5 < x < –2