1314Rev1
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School
Rumson Fair Haven Reg H *
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Course
1314
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
4
Uploaded by CoachRiverTiger30
MATH 1314 – College Algebra – Review Sheet for Exam #1 Show your work on your own paper – you will not receive credit for answers only Do not write on this sheet Know these formulas: Standard equation of circle: (
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
Direct variation: y
=
kx
Slope and Average Rate of Change: y
2
−
y
1
x
2
−
x
1
Linear function: y
=
mx
+
b
or f
(
x
)
=
ax
+
b
Remember, each problem represents a concept to review. Find the standard equation of the circle for problems 1–2: 1) With a radius of 8 and a center of (1, –12) 2) Shown in the graph 3) Find the center and radius of the circle: 81
)
9
(
)
25
(
2
2
=
−
+
+
y
x
For problems 4 – 9, determine whether each of the following relations is a function. Make sure you can explain your answer. 4) 5) y
=
12
x
−
3
6) 7)
8) 9) 10) For the function 11) For the function f
(
x
)
=
x
+
3
a) Find and a) Find f
(
−
1)
and f
(
m
+
6)
b) Find the domain b) Find the domain 12) For the function f
shown: 13) For the function f
shown: a) Find the domain a) Find the domain b) Find the range b) Find the range c) Find
c) Find
f
(0)
f
(
−
2)
x –3 –1 4 3 y 4 2 3 4 x –1 0 –1 3 y –2 –2 0 0
For each function, give intervals where the function is increasing and decreasing. Give your answer in interval notation. 14) 15) 16) Find the average rate of change of f
(
x
)
=
x
2
−
x
+
1
from x
1
=
1
and x
2
=
3
17) Find the average rate of change of x
x
f
+
=
2
)
(
from 2
1
=
x
and 7
2
=
x
Use the tables to evaluate for problems 18–20. 18) a) (
f
+
g
)(1)
b) (
f
−
g
)(0)
c)
19) a)
(
f
/
g
)(3)
b) c) 20) a)
b) d) d)
21) Use the graph to evaluate. a) (
f
−
g
)(0)
b) c) )
2
)(
(
g
f
Use and for problems 22 and 23. 22) a) Find )
)(
(
x
g
f
−
and identify its domain b) Find 23) a) Find )
)(
/
(
x
g
f
and identify its domain b) Find 24) Use x
x
f
=
)
(
and for the following. Simplify your answer. a) Find b) Find c) Find 25) Use the table of f
to determine if
f
is one-to-one and if
f
has an inverse.
x
–1 –2 0 4 f
(
x
)
–5 4 3 4 f
(
x
)
=
x
2
+
3
x
g
(
x
)
=
x
2
−
1
(
f
+
g
)(
−
3)
x
–1 0 1 3 f
(
x
)
2 3 7 12 x
–1 0 1 3 g
(
x
)
–2 –1 0 4
26) Use the graph of
f
to sketch a graph of
f
−
1
. 27) Use the graph of f
to sketch a graph of
f
−
1
. 28)For
2
1
4
)
(
−
=
x
x
f
, find f
−
1
(
x
)
29)
For
f
(
x
)
=
6
x
3
+
5
x
3
, find
f
−
1
(
x
)
30) Use the table of
f
to determine a table of
f
−
1
For problems 31 – 33, find the equation of the line satisfying the conditions. 31) Passing through the points (1.2, –4) and (0.2, 6) 32) Passing through the point (–4, 1), perpendicular to the line y
=
2
x
−
12
33) Horizontal, with y-intercept –8 34) For the linear function f
shown: a) Identify the slope, x
-intercept and y
-intercept b) Write a formula for f
c) Find any zeros of f
35) Let y
vary directly with x
. Find y
when x
=
2.5,
if y
=
13
when x
=
10.
36) Write a formula for a function f
that computes the cost of taking x
credits if credits cost $80 each and fees are fixed at $89. 37) Solve: 3(4
x
−
3)
+
12
=
18
x
−
(6
+
6
x
)
38) Solve: 5
x
−
1
2
(4
−
3
x
)
=
3
2
−
(2
x
+
3)
39) Solve and give your answer in interval notation: 2
4
)
2
1
(
3
+
+
−
≥
−
−
x
x
x
40) Solve and give your answer in interval notation: 1
3
<
2
−
3
x
2
≤
4
3
41) Use the graph of f
and g
to solve the following: a) f
(
x
)
=
g
(
x
)
b) f
(
x
)
<
g
(
x
)
c) f
(
x
)
≥
g
(
x
)
x
–2 0 4 6 f
(
x
)
6 5 3 1
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42) For f
(
x
)
=
2
x
+
1
if
−
3
≤
x
<
0
x
−
1
if
0
≤
x
≤
3
43) For a) Give the domain of f a) Give the domain of f b) Evaluate f
(
−
2)
, f
(0)
and f
(3)
b) Evaluate f
(
−
2)
, f
(0)
and f
(3)
c) Graph f c) Graph f
d) Is f continuous on its domain? d) Is f continuous on its domain? 44) The median US family income between 1980 and 2005 can be modeled by the formula 000
,
20
1450
)
(
+
=
x
x
f
where x is the number of years since 1980. Solve f
(
x
)
=
34,500
and interpret the solution. 45) A 300-gallon tank is initially full of water and is drained at a rate of 10 gallons per minute. a) Write a formula for a linear function W that gives the number of gallons of water in the tank after t
minutes. b) How much water is in the tank after 7 minutes? c) Graph W
and interpret the intercepts. d) Find the domain of W
. 46) Fran jogged 15 miles in 1 hour and 45 minutes. She jogged at 8 miles per hour and then 10 miles per hour. How long did she jog at each speed? 47)In 2010, Medicare spending was $524 billion and in 2020 it is projected to be $949 billion. a) Find a linear function that models the data. Let x represent number of years after 2010. b) Interpret the slope and y-intercept of the graph of f. c) Use your function to estimate Medicare spending in 2016. 48) The weight of an object on Earth is directly proportional to the weight of an object on Mars. If a 25-pound object on Earth weighs 10 pounds on Mars, how much would a 195-pound object on Earth weigh on Mars?