Exam 1 Review
1. Solve the following inequalities and give your answer in interval notation.
𝑎) − 6 − 𝑥 ≥ 2
b)
3(5𝑥 − 6) < 6(3𝑥 + 5)
c)
−2 < 𝑥 − ≤ 3
2. Solve the following absolute value equations for x.
a)
d)
|𝑥 | − 5 = −2
|2(2𝑥 + 3)| − 5 = −1
b) |3𝑥 + 1| = 4
c)
e)
|2𝑥 − 5| = −7
|5𝑥 − 3| − 4 = 3
3. Solve the following absolute value inequalities for x. Give your answer in interval notation.
a)
|𝑥 | + 5 > 2
d) |2𝑥 + 3| − 5 ≤ −1
b) |3𝑥 + 1| ≤ 4
c)
|5𝑥 − 3| − 4 ≥ 3
e) |2𝑥 − 5| > −7
4. What shape do you expect for the graph to be for the following equations? Write the letter (A, B, C, D, E, F, or
G) that corresponds to the shape shown in the table.
A
straight line
𝑦 −4 =𝑥
_______
B
straight HORIZONTAL line
𝑦 = |𝑥 | − 4
_______
C
straight VERTICAL line
𝑦 = 3𝑥 − 4
_______
D
parabola
𝑥 = −9
_______
E
sideways parabola
𝑦 = (𝑥 − 4)
_______
F
V-shaped graph
𝑦=4
_______
G
sideways V-shaped graph
𝑥 = |𝑦| − 4
_______
𝑦= 𝑥 −5
________
9𝑥 − 2𝑦 = 10
________
𝑦= 𝑥
________
5. Graph the following equations using the methods demonstrated in class.
a) 𝑦 = 𝑥 − 2
d) 𝑦 = −3
b) 𝑦 = |𝑥 | − 4
e) 𝑥 = 2
c) 𝑦 = − 𝑥 − 2
f) 𝑥 = 𝑦 − 2
6. State the domain and range of each relation, and then indicate which relations are also functions.
a)
{(3,0), (2, −4), (2,1)}
DOMAIN:
Function?
b)
RANGE:
{(3,0), (4,2), (5,0)}
Function?
DOMAIN:
RANGE:
7. State whether the following graphs represent the graph of a function. Why or why not?
a)
b)
c)
8. Determine the domain and range of the following graphs. Give answers in interval notation.
a)
b)
c)
DOMAIN:
DOMAIN:
DOMAIN:
RANGE:
RANGE:
RANGE:
9. Let 𝒇(𝒙) = 𝟑𝒙𝟐 − 𝟒𝒙 + 𝟏 and 𝒈(𝒙) = 𝟒𝒙 − 𝟑, and evaluate each of the following.
a)
𝑓(0)
b) 𝑓(−2)
d)
𝑓(𝑎 + 2)
e)
𝑔(𝑓(−2))
c)
f)
𝑔(𝑎)
(𝑓 − 𝑔)(𝑥)
10. Find the slope of the line through each of the following pairs of points using the formula for slope.
(You will only be given credit if you show the work for using the slope formula.)
a. (−3, 2) (−1,6)
b. (−2, −1) (3, −5)
c. (−3, 2) (−3,6)
d. (4, 2) (−5,2)
11. What is the slope of the following lines?
a)
Slope: ______________
c) Slope: ______________
b)
Slope: ______________
d) Slope: ______________
Exam 2 Review
1. Graph the following lines using the slope and y-intercept. Tell the slope and y-intercept of each line.
a.
𝑦=− 𝑥−1
b. 4𝑥 − 5𝑦 = 20 Slope = __________
c.
y-intercept = _________
𝑦 = 3𝑥 + 2
Slope = __________
Slope = __________
y-intercept = _________
d. −6𝑥 − 3𝑦 = 9 y-intercept = _________
Slope = __________
y-intercept = _________
e.
𝑦=3
Slope = __________
f. 𝑥 = −5 y-intercept = _________
Slope = __________
y-intercept = _________
2. Find the slope of a line parallel and perpendicular to the following given lines.
a. 𝑦 = −2𝑥 − 5
b. 𝑦 = 2
c. −4𝑥 + 5𝑦 = 20 d.
𝑥 = 12 parallel
= _________
perpendicular
parallel
parallel
parallel
= _________
= _________
= _________
perpendicular
perpendicular
perpendicular
= __________
= __________
= __________
= __________
3. Find the equations of the following lines. Give each answer in slope-intercept form.
a. Find the equation of the line that passes through the point (-2,-5) and has a slope of 2.
Answer: ______________________
b. Find the equation of the line that passes through the points (3,-2) and (-2,1).
Answer: ______________________
c. Find the equation of the line that is parallel to the line 4𝑥 + 5𝑦 = 20 and passes through the point (−1,6).
Answer: ______________________
d. Find the equation of the line that is perpendicular to the line 3𝑥 − 2𝑦 = 12 and passes through the point (3, −5).
Answer: ______________________
4. Graph the solution set of the following linear inequalities.
a. 2𝑥 − 3𝑦 < 6
b. 𝑦 ≤ 2𝑥 − 1
c . 𝑦 ≥ −3
d. 𝑥 < 4