Week in Review # 1
MATH 131
DROST
Algebra Review, 1.1
5. Write the equation of the line passing through the
point (5, −2) that:
a. has an x-intercept of 2.
b. that passes through the origin.
c. that is horizontal.
1. Algebra Review
a) Simplify: 16
− 32
b) Factor: 3x2 − 5x − 2
1
2
c) Simplify:
−
x+3 x
d) Simplify:
√
4
i. x12
√
4
ii. x8
6. Identify each of the following as even functions, odd
functions, or neither.
a. y=x2+5
b. x2 + y2 = 4
c. xy=1
7. Graph: y= (x-4)2 + 5
e) Multiply and simplify:
(3x − 2)(x + 4)
f) Factor completely: x4 − 6x3 + 9x2
g) Tonya had one-third of the problems finished before dinner. After dinner she completed
8 more problems, and then took a break since she
was half way done. How many problems were assigned?
h) Simplify completely:
2x2 − 7x − 4
x2 − 7x + 12
2. Finding the domain of the function
√
a) f (x) = 3 · x2 − 4x + 1
√
b) f (x) = 3 x + 1
√
c) f (x) = x2 − 4
d) f (x) =
−x
x+5
if x < 0


 x+1
x
if x ≥ 2




9. The amount spent annually in college bookstores
in the U.S. is modeled by
f (x) = .19x + 1.6
e) f (x) =| x |
√
x+5
f) f (x) =
x+1
where x is the number of years since 1982, and
f (x) is the amount spent in billions of dollars.
a. How much is the spending increasing
each year?
3. Be able to express your answer in each of the
following forms:
Interval Notation
a. [−4, 3)
b.
c. (−∞, 2]
8. A right rectangular box has a volume of 320 in3. If
the length is 2 in. more than the width, and the depth
is half the width, write an equation (DO NOT
SOLVE) to represent this information.
Inequality Notation
−2 < x ≤ 5
4. Find the average rate of change between the following sets of points:
a. (8, −3) and (5, 2)
b. (a, b − 1) and (a − 1, b + 1)
b. According to this model, how much was
spent in 1990?
√
10. Given f (x) = x2 − 6x + 8, g(x) = 9 − x2 , and
h(x) = x2 − 16.
a. Find (f − h)(x) and state the domain.
f
b. Find
(x) and state the domain.
h
h
c. Find
(x) and state the domain.
g
11. Given: 4x + 2y = 30. If x increases 2a, how is
the y value changed?
12. Name four ways to represent a function.
a.
b.
22. Find the difference quotient for the function
f(x) listed in problem #13.
23. Which of the following are polynomials?
a. 3x−2 + 4x − 12
c.
d.
13. Find the average rate of change for
f (x) = 3x2 − x + 5 when x = 2 and ∆x = 4.
14. Solve the following double inequality for x:
2x − 4 ≤ 36 < 5x + 11
b. πx3 + 4x − 2
√
c. 4 x + 5
2x + 10
d.
x−5
24. Solve for x:
a. 8x+2 = 165−x
b. 25 ∗ 5x = 53x+4
15. Write the expression which represents the
25. If t represents the time in hours spent studying
transformation of the basic square root function with
for the exam,and the average score is described−
the following changes:
by the function N = 25(4 − 3e 0.1t).
a. If a student does not study, what does this
a. shifted left 2 units,
model predict their score will be?
b. reflected about the x-axis,
b. If the time spent studying approaches
c. shifted up 3 units.
infinty, what does this model predict their score
will be?
16. Basic Elementary Functions
Column A
1. f (x) = x2
√
2. g(x) = x
3. h(x) =| x |
4. F (x) = 2x
5. G(x) =
√
x
Column B
a. shaped like a ”v”
b. increasing function,
concave up
c. parabola which opens up
d. half a parabola which
opens to the right
e. increasing function,
concave down
17. Graph the piece-wise defined function
−2x + 4, x ≤ 2
f (x) =
x2 − 1,
x>2
18. T or F: x=4 represents a function.
19. Given the parabola: f (x) = 3x2 − 12x + 2.
a. Find the domain of f (x).
b. Find the range of f (x).
c. Find the vertex.
20. Given: g(x) = 4(x − 2)2 + 5
a. Find the x-intercept.
b. Find the y-intercept.
c. What is the axis of symmetry of g(x)?
21. Find the equation of the parabola which opens
up and has a vertex at (2, −3), and passes
through the point (4, 1).