Math 55
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Chapter2Review-NatalieBanks.pdf
11/22/2020 Chapter 2 Review-Natalie Banks
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1.
Student: Natalie Banks Date: 11/22/20
Instructor: Sam Pearsall Course: Math 55, Oct-Dec F20 Assignment: Chapter 2 Review
Show that each pair is a solution of the equation. Then graph the two pairs to determine another solution.
; , y + 3x = 4 (2, − 2) (4, − 8)
Is the pair a solution?(2, − 2)
No Yes
Is the pair a solution?(4, − 8)
No Yes
Use the points given above and the graphing tool to graph the equation.
Use the graph to determine another solution of . Is the pair a solution?
y + 3x = 4 (0,4)
No Yes
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2
2 4 6 8
10
x
y
YOU ANSWERED:
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
11/22/2020 Chapter 2 Review-Natalie Banks
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2. Graph the equation by plotting points.
y x= 6 − 9
Use the graphing tool on the right to graph the equation.
-20-16-12 -8 -4 4 8 12 16 20
-20 -16 -12 -8 -4
4 8
12 16 20
x
y
YOU ANSWERED:
-20 -16 -12 -8 -4 4 8 12 16 20
-20
-16
-12
-8
-4
4
8
12
16
20
x
y
11/22/2020 Chapter 2 Review-Natalie Banks
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3.
4.
Graph the equation by plotting points.
y x= − 4 3 + 2
Use the graphing tool on the right to graph the equation.
-20-16-12 -8 -4 4 8 12 16 20
-20 -16 -12 -8 -4
4 8
12 16 20
x
y
YOU ANSWERED:
-20 -16 -12 -8 -4 4 8 12 16 20
-20
-16
-12
-8
-4
4
8
12
16
20
x
y
Determine whether the correspondence is a function.
Domain Range
22 5 15
21
9
Is this correspondence a function?
Yes
No
11/22/2020 Chapter 2 Review-Natalie Banks
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5.
6.
7.
Find the function values given the function ( ) . Complete parts (a) through (f) below.k s = 3s + 6
a) ( ) (Simplify your answer.)k 6 = 24
b) ( ) (Simplify your answer.)k − 9 = − 21
c) (Simplify your answer.)k 2 3 = 8
d) (0) (Simplify your answer.)k = 6
e) ( ) (Simplify your answer.)k a − 6 = 3a − 12
f) ( ) (Simplify your answer.)k a + h = 3a + 3h + 6
YOU ANSWERED: − 4
Find the function values given the function (x) x x. Complete parts (a) through (f) below.k = 4 2 − 5
a) ( ) (Simplify your answer.)k 0 = 0
b) ( ) (Simplify your answer.)k 3 = 21
c) ( ) (Simplify your answer.)k − 2 = 26
d) ( ) (Simplify your answer.)k − 1 = 9
e) ( ) (Simplify your answer.)k 10 = 350
f) (Simplify your answer.)k(8a) = 256a − 40a2
YOU ANSWERED: 265(4a
The function A(s) given by A(s) s can be used to estimate the average age of employees of a company in the years 1981 to 2009. Let A(s) be the average age of an employee, and s be the number of years since 1981; that is, s 0 for 1981 and s 9 for 1990. What was the average age of the employees in 2003 and in 2009?
= 0.295 + 51 =
=
The average age of the employees in 2003 is years.57 (Round to the nearest whole number as needed.)
The average age of the employees in 2009 is years.59 (Round to the nearest whole number as needed.)
YOU ANSWERED: 48
64
11/22/2020 Chapter 2 Review-Natalie Banks
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8.
9.
10.
Determine if the graph is a function.
Is this the graph of a function?
No
Yes
-8 8
-8
8
x
y
Determine if the graph is a function.
Is this the graph of a function?
Yes
No
-8 8
-8
8
x
y
Find the domain of the function.
f(x) = 13
x + 13
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is {x | x is a real number and x }.≠ − 13 (Type an integer or a fraction. Use a comma to separate answers as needed.)
B. The domain is {x | }. (Type an inequality or a compound inequality.)
C. The domain is { }. (Type an integer or a fraction. Use a comma to separate answers as needed.)
D. The domain is {x | x is a real number}.
YOU ANSWERED: C.: 10
11/22/2020 Chapter 2 Review-Natalie Banks
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11.
12.
13.
14.
Find the domain of the function f(x).
f(x) = x − 2x + 112
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is .x (Simplify your answer. Type an inequality or a compound inequality.)
B. The domain is .x x is a real number and x ≠ (Simplify your answer. Use a comma to separate answers as needed.)
C. The domain is . (Simplify your answer. Use a comma to separate answers as needed.)
D. The domain is the set of all real numbers.
Find the slope and the y-intercept.
y x= 8 + 2
The slope is .8
The y-intercept is (0, ).2
Find the slope and the y-intercept.
x y2 − 9 = 10
The slope is . 2 9
(Type an integer or a fraction.)
The y-intercept is 0, .− 10 9
YOU ANSWERED: 0
5
Find the slope of the line containing the given pair of points.
( , ) and ( , ) 3 − 9 8 − 3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is m . (Simplify your answer.)= 6 5
B. The slope is undefined.
YOU ANSWERED: A.: − 12
5
11/22/2020 Chapter 2 Review-Natalie Banks
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15.
16.
Find the intercepts and then use them to graph the equation.
x y4 + 2 = 8
Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2
2 4 6 8
10
x
y
YOU ANSWERED:
-10 -8 -6 -4 -2 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
Find the intercepts and then use them to graph the equation.
y x2 = − 6 + 3
Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2
2 4 6 8
10
x
y
11/22/2020 Chapter 2 Review-Natalie Banks
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17.
18.
Graph the equation using the slope and the y-intercept.
y x= 5 4 + 7
Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.
-20-16-12 -8 -4 4 8 12 16 20
-20 -16 -12 -8 -4
4 8
12 16 20
x
y
YOU ANSWERED:
-20 -16 -12 -8 -4 4 8 12 16 20
-20
-16
-12
-8
-4
4
8
12
16
20
x
y
Graph the following equation and if possible, determine the slope.
x = − 4
Use the graphing tool on the right to graph the equation.
What is the slope of the line?
A. m = (Type an integer or a fraction.)
B. The slope is not defined.
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2
2 4 6 8
10
x
y
11/22/2020 Chapter 2 Review-Natalie Banks
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19.
20.
21.
22.
Graph the following equation and if possible, determine the slope.
f(x) = 3
Use the graphing tool on the right to graph the equation.
What is the slope of the line?
A. m = 0 (Simplify your answer.)
B. The slope is not defined.
-10 -8 -6 -4 -2 2 4 6 8 10
-10 -8 -6 -4 -2
2 4 6 8
10
x
y
Determine whether the graphs of the two equations are perpendicular.
x 2y+ = 3 2x 4y+ = 7
Are the graphs of the given equations perpendicular?
No
Yes
Determine whether the graphs of each pair of lines are parallel.
x y2 + 8 = 2y x= 4 − 3
Are the graphs of the given equations parallel?
Yes
No
Determine whether the graphs of the pair of lines are parallel.
x + 9 y= y x− = − 5
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope of the line x y is .+ 9 = 1
B. The slope of the line x y is undefined.+ 9 =
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope of the line y x is .− = − 5 1
B. The slope of the line y x is undefined.− = − 5
Are the graphs of the given equations parallel?
No
Yes
11/22/2020 Chapter 2 Review-Natalie Banks
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23.
24.
25.
26.
27.
Determine whether the graphs of the given pair of lines are perpendicular.
x2 = 3 y− 5 = 10
Are the graphs of the given equations perpendicular?
Yes
No
Find the slope-intercept equation of the line that has the given characteristics.
Slope and y-intercept (0, )1.3 − 1
The slope-intercept equation y .= 1.3x − 1 (Use integers or decimals for any numbers in the expression.)
YOU ANSWERED: 1
Find an equation of the line having the given slope and containing the given point.
m , ( , )= − 6 7 9
The equation of the line is y . = − 6x + 51 (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)
YOU ANSWERED: 6x + 39
Find an equation of the line containing the given pair of points.
( , ) and ( , )1 2 3 3
y = x + 1 2
3 2
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)
Write an equation of the line containing the given point and parallel to the given line.
( , ); x y7 − 8 7 − 2 = 3
The equation of the line is y .= x − 7 2
65 2
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)
YOU ANSWERED: 3
11/22/2020 Chapter 2 Review-Natalie Banks
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28.
29.
Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y mx b.= +
( , ); x y2 7 5 + = 4
The equation of the line is y .= (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Assume that a constant rate of change exists for the model formed. The table lists data regarding the average salaries of several professional athletes in the years 1991 and 2001. a) Use the two data points to find a linear function that fits the data. Let x the number of years after 1990 and S(x) the average salary.
= =
b) Use the function of part (a) to estimate the average salary in 2005. Predict the average salary in 2010.
Year, x (in number of years
after 1990) Average Salary
1991, 1 $274,000 2001, 11 $1,380,000
a) A linear function that fits the data is S(x) .= 110,600x + 163,400 (Use integers or decimals for any numbers in the expression.)
b) The predicted average salary for 2005 is $ .1,822,400 (Round to the nearest whole number as needed.)
The predicted average salary for 2010 is $ .2,375,400 (Round to the nearest whole number as needed.)
YOU ANSWERED: 2
1500000
3,000,000
