Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 4
Linear
Functions,
Their
Properties and
Linear Models
© 2009 Pearson Education, Inc.
All rights reserved.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 1
Determine the slope and y-intercept of the
8
function f x    x  4.
7
a.
b.
c.
d.
8
m  ; b  4
7
8
m  4; b  
7
7
m ; b4
8
8
m ; b4
7
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 2
Determine the slope and y-intercept of the
8
function f x    x  4.
7
a.
b.
c.
d.
8
m  ; b  4
7
8
m  4; b  
7
7
m ; b4
8
8
m ; b4
7
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 3
1
Graph h x    x  3.
2
a.
b.
c.
Copyright © 2009 Pearson Education, Inc.
d.
Slide 4 - 4
1
Graph h x    x  3.
2
a.
b.
c.
Copyright © 2009 Pearson Education, Inc.
d.
Slide 4 - 5
Determine the average rate of change for the
2
function f x   x  3.
5
a.
b.
2

5
2
5
c.
3
d.
3
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 6
Determine the average rate of change for the
2
function f x   x  3.
5
a.
b.
2

5
2
5
c.
3
d.
3
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 7
3
Graph h x   x  3. State whether it is
4
increasing, decreasing, or constant.
a. decreasing
b. increasing
c. increasing
d. increasing
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 8
3
Graph h x   x  3. State whether it is
4
increasing, decreasing, or constant.
a. decreasing
b. increasing
c. increasing
d. increasing
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 9
To convert a temperature from degrees Celsius
to degrees Fahrenheit, you multiply the
temperature in degrees Celsius by 1.8 and then
add 32 to the result. Express F as a linear
function of C.
a.
F c   1.8c  32
b.
F c   1.8  32c
c.
F c   33.8c
d.
c  32
F c  
1.8
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 10
To convert a temperature from degrees Celsius
to degrees Fahrenheit, you multiply the
temperature in degrees Celsius by 1.8 and then
add 32 to the result. Express F as a linear
function of C.
a.
F c   1.8c  32
b.
F c   1.8  32c
c.
F c   33.8c
d.
c  32
F c  
1.8
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 11
The cost of a taxi ride is computed as follows:
there is a fixed charge of $2.80 as soon as you
get in the taxi, to which a charge of $2.45 per
mile is added. Find the equation of the cost,
C(x), an x mile taxi ride.
a.
C x   2.45  2.80x
b.
C x   2.80  2.45x
c.
C x   5.25x
d.
C x   3.75x
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 12
The cost of a taxi ride is computed as follows:
there is a fixed charge of $2.80 as soon as you
get in the taxi, to which a charge of $2.45 per
mile is added. Find the equation of the cost,
C(x), an x mile taxi ride.
a.
C x   2.45  2.80x
b.
C x   2.80  2.45x
c.
C x   5.25x
d.
C x   3.75x
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 13
Find the equation of the line containing the
points (2, 1.2) and (9, 4.3) and graph the line on
a scatter diagram of the given data.
a.
c.
y  0.49x  0.31
y  0.44x  0.31
Copyright © 2009 Pearson Education, Inc.
b.
d.
y  0.37x  0.47
y  0.44x  0.37
Slide 4 - 14
Find the equation of the line containing the
points (2, 1.2) and (9, 4.3) and graph the line on
a scatter diagram of the given data.
a.
c.
y  0.49x  0.31
y  0.44x  0.31
Copyright © 2009 Pearson Education, Inc.
b.
d.
y  0.37x  0.47
y  0.44x  0.37
Slide 4 - 15
The table gives the times spent watching TV and
the grades of several students. Plot and interpret
the appropriate scatter diagram.
Weekly TV (h) 6
12
18
24
Grade (%)
92.5 87.5 72.5 77.5
a. More hours
watching TV
may reduce
grades
b. More hours
watching TV
may increase
grades
c. More hours
watching TV
may reduce
grades
d. More hours
watching TV
may increase
grades
Copyright © 2009 Pearson Education, Inc.
30
62.5
36
57.5
Slide 4 - 16
The table gives the times spent watching TV and
the grades of several students. Plot and interpret
the appropriate scatter diagram.
Weekly TV (h) 6
12
18
24
Grade (%)
92.5 87.5 72.5 77.5
a. More hours
watching TV
may reduce
grades
b. More hours
watching TV
may increase
grades
c. More hours
watching TV
may reduce
grades
d. More hours
watching TV
may increase
grades
Copyright © 2009 Pearson Education, Inc.
30
62.5
36
57.5
Slide 4 - 17
Determine if the type of
relation is linear,
nonlinear, or none.
a. Linear
b. Nonlinear
c. None
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 18
Determine if the type of
relation is linear,
nonlinear, or none.
a. Linear
b. Nonlinear
c. None
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 19
Identify the scatter diagram of the relation that
appears linear.
a.
b.
c.
Copyright © 2009 Pearson Education, Inc.
d.
Slide 4 - 20
Identify the scatter diagram of the relation that
appears linear.
a.
b.
c.
Copyright © 2009 Pearson Education, Inc.
d.
Slide 4 - 21
Use a graphing utility to find the equation of the
line of best fit. Round to two decimal places, if
necessary.
x
6
8
20 28 36
y
2
4
13 20 30
a.
y  0.95x  2.79
b.
y  0.90x  3.79
c.
y  0.80x  3.79
d.
y  0.85x  2.79
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 22
Use a graphing utility to find the equation of the
line of best fit. Round to two decimal places, if
necessary.
x
6
8
20 28 36
y
2
4
13 20 30
a.
y  0.95x  2.79
b.
y  0.90x  3.79
c.
y  0.80x  3.79
d.
y  0.85x  2.79
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 23
Match the graph to one
of the listed functions.
a.
y  x 2  10x
b.
y  x 2  10x
c.
y  x  10x
d.
y  x 2  10x
2
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 24
Match the graph to one
of the listed functions.
a.
y  x 2  10x
b.
y  x 2  10x
c.
y  x  10x
d.
y  x 2  10x
2
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 25
Use transformations of the graph of y = x2 to
graph f (x) = 3x2 – 6.
a.
b.
c.
d.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 26
Use transformations of the graph of y = x2 to
graph f (x) = 3x2 – 6.
a.
b.
c.
d.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 27
Find the vertex and axis of symmetry of the
2
graph of the function f x  3x  18x.

a.
3,0;
b.
3,27 ;
c.
3,27;
x3
d.
3,0;
x  3
x3
Copyright © 2009 Pearson Education, Inc.
x  3
Slide 4 - 28
Find the vertex and axis of symmetry of the
2
graph of the function f x  3x  18x.

a.
3,0;
b.
3,27 ;
c.
3,27;
x3
d.
3,0;
x  3
x3
Copyright © 2009 Pearson Education, Inc.
x  3
Slide 4 - 29
Graph the function f (x) = –x2 – 6x – 5 using its
vertex, axis of symmetry, and intercepts.
a.
b.
c.
d.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 30
Graph the function f (x) = –x2 – 6x – 5 using its
vertex, axis of symmetry, and intercepts.
a.
b.
c.
d.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 31
Find the domain and range of f (x) = x2 – 4x + 3.
a. Domain: all real numbers
Range: {y | y ≥ –1}
b. Domain: {x | x ≥ –2}
Range: {y | y ≥ –1}
c. Domain: all real numbers
Range: {y | y ≤ 1}
d. Domain: all real numbers
Range: all real numbers
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 32
Find the domain and range of f (x) = x2 – 4x + 3.
a. Domain: all real numbers
Range: {y | y ≥ –1}
b. Domain: {x | x ≥ –2}
Range: {y | y ≥ –1}
c. Domain: all real numbers
Range: {y | y ≤ 1}
d. Domain: all real numbers
Range: all real numbers
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 33
Determine where the function f (x) = –x2 – 2x + 8
is increasing and decreasing.
a. Increasing on (–1, ∞)
Decreasing on (–∞, –1)
b. Increasing on (–∞, –1)
Decreasing on (–1, ∞)
c. Increasing on (–∞, 9)
Decreasing on (9, ∞)
d. Increasing on (–9, ∞)
Decreasing on (–∞, 9)
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 34
Determine where the function f (x) = –x2 – 2x + 8
is increasing and decreasing.
a. Increasing on (–1, ∞)
Decreasing on (–∞, –1)
b. Increasing on (–∞, –1)
Decreasing on (–1, ∞)
c. Increasing on (–∞, 9)
Decreasing on (9, ∞)
d. Increasing on (–9, ∞)
Decreasing on (–∞, 9)
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 35
Determine the maximum or minimum value of
the quadratic function f (x) = 2x2 – 2x + 9 .
a. Minimum value is
b. Maximum value is
c. Minimum value is
d. Maximum value is
Copyright © 2009 Pearson Education, Inc.
19

2
19

2
1
2
1
2
Slide 4 - 36
Determine the maximum or minimum value of
the quadratic function f (x) = 2x2 – 2x + 9 .
a. Minimum value is
b. Maximum value is
c. Minimum value is
d. Maximum value is
Copyright © 2009 Pearson Education, Inc.
19

2
19

2
1
2
1
2
Slide 4 - 37
The owner of a video store has determined that
the profits P of the store are approximately given
by P (x) = –x2 + 50x + 53. Where x is the number
of videos rented daily. Find the maximum profit
to the nearest dollar.
a. $678
b. $625
c. $1303
d. $1250
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 38
The owner of a video store has determined that
the profits P of the store are approximately given
by P (x) = –x2 + 50x + 53. Where x is the number
of videos rented daily. Find the maximum profit
to the nearest dollar.
a. $678
b. $625
c. $1303
d. $1250
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 39
Alan is building a garden shaped like a rectangle
with a semicircle attached to one short side. If he
has 30 feet of fencing to go around it, what
dimensions will give him maximum area?
60
a. L: 10.8 ft; W :
 8.4 ft
4
30
 4.2 ft
b. L: 8.4 ft; W :
4
60
 5.4 ft
c. L: 8.1 ft; W :
 8
60
 8.4 ft
d. L: 4.2 ft; W :
4
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 40
Alan is building a garden shaped like a rectangle
with a semicircle attached to one short side. If he
has 30 feet of fencing to go around it, what
dimensions will give him maximum area?
60
a. L: 10.8 ft; W :
 8.4 ft
4
30
 4.2 ft
b. L: 8.4 ft; W :
4
60
 5.4 ft
c. L: 8.1 ft; W :
 8
60
 8.4 ft
d. L: 4.2 ft; W :
4
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 41
You have 96 feet of fencing to enclose a
rectangular plot that borders on a river. If you do
not fence the side along the river, find the length
and width of the plot that will maximize the area.
a. length: 72 ft, width: 24 ft
b. length: 48 ft, width: 24 ft
c. length: 48 ft, width: 48 ft
d. length: 24 ft, width: 24 ft
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 42
You have 96 feet of fencing to enclose a
rectangular plot that borders on a river. If you do
not fence the side along the river, find the length
and width of the plot that will maximize the area.
a. length: 72 ft, width: 24 ft
b. length: 48 ft, width: 24 ft
c. length: 48 ft, width: 48 ft
d. length: 24 ft, width: 24 ft
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 43
An engineer collects data showing the speed s of a
car model and its average miles per gallon M. Use
a graphing calculator to plot the scatter diagram
and find the quadratic function of best fit.

a.
M s  0.063x 2  0.720x  5.143
b.
M s  0.631x  0.720x  5.143
c.
M s  0.0063x  0.720x  5.143
d.
M s  6.309x  0.720x  5.143

2


Copyright © 2009 Pearson Education, Inc.
2
2
Slide 4 - 44
An engineer collects data showing the speed s of a
car model and its average miles per gallon M. Use
a graphing calculator to plot the scatter diagram
and find the quadratic function of best fit.

a.
M s  0.063x 2  0.720x  5.143
b.
M s  0.631x  0.720x  5.143
c.
M s  0.0063x  0.720x  5.143
d.
M s  6.309x  0.720x  5.143

2


Copyright © 2009 Pearson Education, Inc.
2
2
Slide 4 - 45
Use the figure to
solve the inequality.
x  1  x  2; 1,2
b. x  1  x  2; 1,2
c. x x  1 or x  2; ° ,1 or 2,° 
d. x x  1 or x  2; ° ,1 or  2,° 
a.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 46
Use the figure to
solve the inequality.
x  1  x  2; 1,2
b. x  1  x  2; 1,2
c. x x  1 or x  2; ° ,1 or 2,° 
d. x x  1 or x  2; ° ,1 or  2,° 
a.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 47
Solve the inequality.
x 2  6x  7  0
a.
x  7  x  1;7,1
b.
 x x  7 or x  1;  , 7  or 1,  
c.
 x x  7;  , 7 
d.
 x x  1; 1,  
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 48
Solve the inequality.
x 2  6x  7  0
a.
x  7  x  1;7,1
b.
 x x  7 or x  1;  , 7  or 1,  
c.
 x x  7;  , 7 
d.
 x x  1; 1,  
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 49
The revenue achieved by selling x graphing
calculators is figured to be x(38 – 0.2x) dollars.
The cost of each calculator is $22. How many
graphing calculators must be sold to make a profit
(revenue – cost) of at least $295.80?
a.
b.
c.
d.
x 29  x  51;29,51
x 9  x  31;9,31
x 30  x  28;30,28
x 31  x  49;31,49
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 50
The revenue achieved by selling x graphing
calculators is figured to be x(38 – 0.2x) dollars.
The cost of each calculator is $22. How many
graphing calculators must be sold to make a profit
(revenue – cost) of at least $295.80?
a.
b.
c.
d.
x 29  x  51;29,51
x 9  x  31;9,31
x 30  x  28;30,28
x 31  x  49;31,49
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 51
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