```Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 4
Linear
Functions,
Their
Properties and
Linear Models
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
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
Slide 4 - 3
1
Graph h x    x  3.
2
a.
b.
c.
d.
Slide 4 - 4
1
Graph h x    x  3.
2
a.
b.
c.
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
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
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
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
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
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
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
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
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
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
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
92.5 87.5 72.5 77.5
a. More hours
watching TV
may reduce
b. More hours
watching TV
may increase
c. More hours
watching TV
may reduce
d. More hours
watching TV
may increase
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
92.5 87.5 72.5 77.5
a. More hours
watching TV
may reduce
b. More hours
watching TV
may increase
c. More hours
watching TV
may reduce
d. More hours
watching TV
may increase
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
Slide 4 - 18
Determine if the type of
relation is linear,
nonlinear, or none.
a. Linear
b. Nonlinear
c. None
Slide 4 - 19
Identify the scatter diagram of the relation that
appears linear.
a.
b.
c.
d.
Slide 4 - 20
Identify the scatter diagram of the relation that
appears linear.
a.
b.
c.
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
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
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
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
Slide 4 - 25
Use transformations of the graph of y = x2 to
graph f (x) = 3x2 – 6.
a.
b.
c.
d.
Slide 4 - 26
Use transformations of the graph of y = x2 to
graph f (x) = 3x2 – 6.
a.
b.
c.
d.
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
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
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.
Slide 4 - 30
Graph the function f (x) = –x2 – 6x – 5 using its
vertex, axis of symmetry, and intercepts.
a.
b.
c.
d.
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
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
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)
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)
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
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
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
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
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
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
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
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
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


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


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.
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.
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,  
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,  
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
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
Slide 4 - 51
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