practice exercises 5_MAT-1210-GS-sep22
docx
keyboard_arrow_up
School
Thomas Edison State College *
*We aren’t endorsed by this school
Course
121
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
11
Uploaded by MegaFlowerDove26
MAT-1210: COLLEGE ALGEBRA
Kristi Stevenson
Practice Exercises 5
SECTION 3.5
Algebraic
For the following exercise, write a formula for the function obtained when the graph is shifted as described.
1.
f
(
x
)=
1
x
is shifted down 4 units and to the right 3 units.
For the following exercise, describe how the graph of the function is a transformation of the graph of the original function f
.
2.
y
=
f
(
x
−
2
)+
3
The function has shifted left 2 units and up three units.
Graphical
For the following exercise, use the graph f
(
x
)=
2
x
of shown in the figure below to sketch a graph of the transformation of the f(x)
.
3.
g
(
x
)=
2
x
+
1
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, sketch a graph of the function as a transformation of the graph of one of the toolkit functions.
4.
m
(
t
)=
3
+
√
t
+
2
For the following exercise, write an equation for the graphed function by using transformations of the graphs of one of the toolkit functions.
5.
y
=(
x
−
1
)
2
−
3
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, use the graph of the transformed toolkit function to write a formula for the resulting function.
6.
y
=
(
−
x
+
2
)
3
+
1
For the following exercise, determine whether the function is odd, even, or neither.
7.
h
(
x
)=
2
x
−
x
3
For the following exercise, describe how the graph of the function is a transformation of the graph of the original function f
.
8.
g
(
x
)=
f
(
1
5
x
)
❑
g(x) = f (bx) The graph is being horizontal compression by a factor of 5 since b is greater than 1.
For the following exercise, write a formula for the function that results when the graph of a given toolkit function is transformed as described.
9.
The graph of f
(
x
)=
1
x
is vertically stretched by a factor of 8, then shifted to the right 4 units and up 2 units.
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
f
(
x
)
=
8
(
1
x
−
4
)
+
2
For the following exercise, describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.
10.
q
(
x
)=
(
1
4
x
)
3
+
1
This is horizontal shift of 1 unit and a horizontal compression by a factor of 4.
SECTION 4.1
For the following exercise, determine whether the equation of the curve can be written as a linear function.
11.
3
x
2
+
5
y
=
15
Not a linear function – y
=
3
5
x
2
+
3
For the following exercise, determine whether the function is increasing or decreasing.
12.
h
(
x
)−
2
x
+
4
This doesn’t have an equals sign so I am going to assume that was just a typo and it is supposed to be negative 2 and not equals 2.
Since m
is negative this is a decreasing function.
For the following exercise, find the slope of the line that passes through the two given points.
13.
(−
1,4
)∧
(
5,2
)
For the following exercise, find a linear equation satisfying the conditions, if possible.
14.
f
(−
1
)=
4
∧
f
(
5
)=
1
(-1,4) (5,1)
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, determine whether the lines given by the equations are parallel, perpendicular, or neither
15.
3
y
+
x
=
12
∧−
y
=
8
x
+
1
Neither For the following exercise, find the x- and y-intercepts of the equation.
16.
7
x
+
2
y
=
56
For the following exercise, use the descriptions of the pair of lines to find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?
17.
Line 1: Passes through (1,7) and (5,5). Line 2: Passes through (-1,-3) and (1,1)
For the following exercise, write an equation for the line described.
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
18.
Write an equation for a line perpendicular to h
(
t
)=−
2
t
+
4
and passing through the point (-
4,-1).
For the following exercise, write an equation for the line graphed.
19.
For the following exercise, sketch a line with the given features.
20. A y
-intercept of (0,5) and slope −
3
2
.
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, write the equation of the line shown in the graph.
21. f(x) = 2
SECTION 4.2
For the following exercise, consider this scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5,900. By 2012 the population had dropped to 4,700. Assume this trend continues.
22.
Identify the year in which the population will reach 0.
For the following exercise, consider this scenario: The number of people afflicted with the common cold in
the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were afflicted.
23.
Find a reasonable domain and range for the function.
x
year
s
x
0
x
1
x
2
x
3
x
4
x
5
Domain = 0 ≤ x ≤ 5
Range = This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
Real-World Applications
24.
In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured to be 285. The population changed linearly. Let the input be years since 2003.
a.
Find a formula for the owl population, P
. Let the input be years since 2003.
b.
What does your model predict the owl population to be in 2012?
The owl population in 2012 will be 216.
25.
When hired at a new job selling electronics, you are given two pay options:
Option A: Base salary of $10,000 a year with a commission of 9% of your sales.
y = .09s + 10,000
Option B: Base salary of $19,000 a year with a commission of 4% of your sales.
y = .04s + 19,000
Write a model for each option. How much would you need to sell for option A to produce a larger income?
Option A would need to sell more than $180,000 electronics to have a larger income than Option B.
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
SECTION 4.3
For the following exercise, draw a scatter plot for the data provided. Does the data appear to be linearly related?
26.
100
250
300
450
600
750
12
12.6
13.1
14
14.5
15.2
The data is linearly related.
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
For the following exercise, draw a best-fit line for the plotted data.
27.
Numeric
28.
The U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data for several years is given in the table below. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the percentage exceed 35%?
Year
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Percent Graduates
21.3
21.4
22.2
23.6
24.4
25.6
26.7
27.7
28
29.4
Yes, the trend appears linear, and the percentage should exceed 35% in 2020.
For the following exercise, consider this scenario: The population of a city increased steadily over a 10-
year span. The following ordered pairs shows the population and the year over the 10-year span (population, year) for specific recorded years:
(
2500,2000
)
,
(
2650,2001
)
,
(
3000,2003
)
,
(
3500,2006
)
,
(
4200,2010
)
29.
Use linear regression to determine a function, y
, where the year depends on the population. Round to three decimal places of accuracy. Predict when the population will hit 8,000.
The population will hit 8,000 in 2032.771
This work, “Practice Exercises 5,” is a derivative of College Algebra 2e
by Jay Abramson, OpenStax used under CC BY 4.0
. “Practice Exercises 5” is licensed under CC BY 4.0 by Thomas Edison State University.
y=2032.771