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WorksheetsUnit. 4: Linear Functions TEST REVIEW
Total questions: 150
Worksheet time: 7hrs 10mins
Identify the domain of the function.
[−2,3]
(−2,3)
[−5,5]
(−5,5)
Identify the range of the function.
[−2,3]
(−2,3)
[−5,5]
(−5,5)
Identify the y-intercept of the function.
y=5
y=1
y=0.5
x=0.5
Describe the function between x=−2 and x=2 .
Increasing
Decreasing
Constant
Identify the domain of the function.
[−1,3]
(−1,3]
(−1,3)
[−1,3)
Identify the range of the function.
[−5,3)
[−5,4)
[−5,4]
(−5,4)
Identify the x-intercept of the function.
x=2
x=0
x=−1
x=3
Identify the y-intercept of the function.
y=−5
y=0
y=3
y=4
Identify the minimum of the function.
y=−5
y=0
y=3
y=4
Identify the maximum of the function.
y=−5
y=0
y=3
y=4
Describe the function between x=0 and x=2 .
Increasing
Decreasing
Constant
Identify the domain of the function.
(1,∞)
[1,∞)
(2,∞)
[2,∞)
Identify the range of the function.
(1,∞)
[1,∞)
(2,∞)
[2,∞)
Describe the function between x=2 and x=6 .
Increasing
Decreasing
Constant
Identify the domain of the function.
[−4,4]
(−∞,∞)
[−4,∞)
[−∞,4]
Identify the range of the function.
[−4.5,2]
(−∞,∞)
[−4.5,∞)
[−∞,2]
Identify the x-intercept(s) of the function.
x=−2
x=−4
x=−4,−1
x=−4,−1,4
Identify the y-intercept(s) of the function.
y=−2
y=2,−2, −4.5
y=−4
None
Identify the relative maximum of the function.
y=−2
y=2
y=−4
None
Describe the function between x=3 and x=5 .
Increasing
Decreasing
Constant
Find the function's x- and y-intercepts.
x-int (0,-3) and (0,1)
y-int (-4,0)
x-int (-3,0) and (1,0)
y-int (0,-4)
x-int (-4, 1)
y-int (-4, ∞)
x-int (-3,0) and (1,0)
y-int (0,-3)
Find the function's maximum and minimum points
no maximum
minimum (-4,-1)
no minimum
maximum (-3, 1)
no maximum
minimum (-1,-4)
maximum (-3,1)
minimum (0,-3)
Identify where the function is increasing and where it is decreasing.
increasing x > -1 and decreasing x<-1
increasing x < -1 and decreasing x > -1
increasing ꓣ and decreasing nowhere
increasing -1 < x < 4 and decreasing -3 < x < 1
Identify the intervals where the function is positive and where it is negative.
positive x > -1 and negative x < -1
positive nowhere and negative -4 < x < -1
positive x < -3 and x > 1 and negative -3 < x < 1
positive R and negative x < -4
What was the initial height of the projectile?
50
0
200
6.75
What is the maximum height?
200
50
3
0
Which coordinate is a relative maximum for the graph?
None
(0,4)
(3,1)
(1, -1)
Which coordinate is a relative minimum of the graph?
None
(0,4)
(3,1)
(1, -1)
What is the domain of the function?
x≤5
x<5
x≤2
x<2
What is the range of the function?
y≤5
y < 5
y≤2
y < 2
y-intercept on a graph?
On what interval is the graph decreasing?
y>3
y<3
y≥3
y≤3
On which interval is the graph increasing?
−5≤x≤−3
−3≤x≤−1
1≤x≤4
x≥5
What is the RANGE?
−3<y≤3
All Real Numbers
−4≤y≤5
y≤−4
What is the DOMAIN?
x≥0
x<0
All Real Numbers
{0, 1, 2, 3, 4,...}
Describe the function between x=−2 and x=2 .
Increasing
Decreasing
Constant
Identify the domain of the function.
−4≤x≤4
R
x≥4
x≤4
Identify the range of the function.
−4.5≤y≤2
R
y≥−4.5
y≤2
What is the average rate of change of f(x) on the interval [-3, -2].
Calculate the average rate of change from 20 to 40 minutes.
-2 minutes per gallon
-20 minutes per gallon
-2 gallons per minute
-20 gallons per minute
If a question asks you to find f(2), what does that mean?
Let x = 2
Let y = 2
Find the average rate of change of f(x)=2x2+3x-1 from 1 to 2.
18
-9
9
3
Given the function g(x)=x-1 and the range {-1, 1, 2}, what is the domain?
{0, 2, 3}
{-2, 0, 1}
{-1, 1, 2}
{2, 0, 1}
What is the rate of change for the following graph?
80
40
20
160
What is the average rate of change of 1 ≤ x5?
-0.65
-0.75
3.75
4
Using the graph of the quadratic function, identify the y-intercept.
(4, -6)
(0, 2)
(.5, 0)
(7.5, 0)
What is the range?
x≥0
y≥0
All real numbers
{0, 1, 2, 3, 4,...}
What is the average rate of change of f(x) on the interval [-3, -2].
Which equation represents slope-intercept form?
y=mx+b
Ax+By=C
m=x2−x1y2−y1
y−y1=m(x−x1)
What TWO things do you need to write a linear equation? Check both things!
Slope
Y-intercept
Y - axis
Standard form
What is the x-intercept of the linear equation: y=2x−6
-6
6
3
It's impossible to tell.
Write an equation of the line in slope-intercept form.
y=21x+4
y=−2x+4
y=−21x+4
y=2x+4
Write the equation given the points (2, 4) and (0,3)
y=-1/2x+3
y=1/2x+3
y=2/1x+3
y=-2/1x+3
(3, -5) and (5, - 1)
What is the slope of this line?
-1/3
1/3
-3
3
What is the equation of the line shown?
y=2x+1
y=-2x+1
y=x+2
y=-2x-1
Graph the given equation using the slope intercept form method:
y=31x−5Which graph represents the table?
Which graph represents the table?
Determine the slope and y-intercept from the following equation: y = 4/3x - 9
slope: 4/3
y-intercept:
(0, -9)
slope: 4/3
y-intercept:
(-9, 0)
slope: -9
y-intercept:
(0,4/3)
slope: -9
y-intercept:
(4/3, 0)
Which of the linear equations below is solved by both (−9, 11) and (−2, 4) ?
y = (−2/9)x + 11
y = x - 2
y = −x + 2
y = −11x + 2/9
Level 1: For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?
(-4, 3)
(3, -4)
(-3, -4)
(-4, -3)
What is the y-intercept of the line?
(0, 1/2)
(0, 1)
(0, -1/2)
(0, -1)
The Roaming Cell Phone Company charges $15.00 flat fee plus $0.20 per minute. If Juanita uses x minutes, what is an equation that can be used to determine her monthly cell phone bill (C)?
The Roaming Cell Phone Company charges $15.00 flat fee plus $0.20 per minute. The equation can be used to determine her monthly cell phone bill is C=0.20x+15. What is the slope for the given equation and what does it represent?
0.20 is the slope. It represents the flat fee.
15 is the slope. It represents the cost per minute.
0.20 is the slope. It represents the cost per minute.
15 is the slope. It represents the flat fee.
The Roaming Cell Phone Company charges $15.00 flat fee plus $0.20 per minute. The equation can be used to determine her monthly cell phone bill is C=0.20x+15. What is the y-intercept for the given equation and what does it represent?
0.20 is the yintercept. . It represents the flat fee.
15 is the y-intercept. It represents the cost per minute.
0.20 is the y-intercept. It represents the cost per minute.
15 is the y-intercept. It represents the flat fee.
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation, where x is the number of months and y is the total cost.
y=30x+4
y=4x+30
y=30x-4
y=4x-30
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. The equation, y=4x+30, represents the total cost, y, each month, x. After how many months will the total cost be $58?
In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. The equation, y=4x+30, represents the total cost, y, each month, x. If Ms. Kurian wants to join the class for 9 months, how much will it cost her?
$36
$6
$274
$66
A holiday meal costs $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs, y, including delivery, for x people?
y = 12.5x - 30
y=30x-12.5
Bob has $150 in his savings account and saves $40 per month. Which equation represents the total amount, y, Bob has in his account after x months?
y=40x-150
Bob has $150 in his savings account and saves $40 per month. The equation, y=40x+150 represent the total amount saved, y, after each month, x. What is the slope for the equation and what does it represent for this problem?
40, how much money Bob saves each month.
40, the starting amount in his savings account.
150, how much money Bob saves each month.
150, the starting amount of his saving account.
Bob has $150 in his savings account and saves $40 per month. The equation, y=40x+150 represent the total amount saved, y, after each month, x. What is the y-intercept for the equation and what does it represent for this problem?
40, how much money Bob saves each month.
40, the starting amount in his savings account.
150, how much money Bob saves each month.
150, the starting amount of his saving account.
The total cost (y) at Six Flags can be modeled by y=1.5x+20 where x is the number of rides you ride. Splash Down Dune's can be modeled by y = 2.4x + 15. with the same definitions for x and y. Which has a greater entrance fee?
Six Flags
Splash Down Dunes
They are the same
Derrick started up a charity for the local animal shelters. He started selling handmade dog leashes for $5. He spends $120 to get the supplies to make the leashes. Write an equation for the amount of money he raises, y, if he sells x amount of leashes.
y=5x+120
y = 120x + 5
y = 5x-120
y = 120 - 5x
Belinda's car needed repairs. The mechanic charged him $140 for the parts and an additional $48 an hour for labor. Write an equation that models this situation.
y = 140x +48
y = -48x +140
y = 48x +140
y = 48x
A pizza shop charges $12 per pizza and a delivery fee of $4.
Which equation represents the cost, c, for any number of pizzas, p?
c = 4p + 12
c = 12p + 4
c = 16p
p = 12 + 4 + c
A car rental company charges $56 plus $0.30 per mile driven.
Write a linear function to model this situation.
y = 56x + 0.30
56x + 0.30y = 86
y = 0.30x + 56
y = 56 - 0.30x
A man is climbing down from 100 feet high descending 30 feet per minute. Which function models his descent?
y = 100 - 30x
y = 100 + 30x
y = 100x + 30
y = 100x - 30
y = -3.8x + 290
Derrick started a new job at McDonald's. He makes $10 per hour. Which graph models his total weekly earnings in terms of the number of hours he works?
Derrick started a new job at McDonald's. He makes $10 per hour. What is the independent variable?
number of hours
amount paid
Abby decides to get a magazine subscription. It costs her $2 per magazine plus an initial fee of $3. Define the variables
y=the cost, x=the number of magazines
y=the number of magazines, y=the cost
Sarah is bringing treats to her elementary school class on her birthday. The number of treats she brings in is based on the number of students in her class.
t = the number of treats
s = the number of students
Which of the variables is INDEPENDENT?
s
t
Jimmy earned $8 for every pizza he delivers.
m = money (dollars)
p = number of pizzas delivered
The dependent variable is:
m = money
p = number of pizzas delivered
Emma gets one sticker for every paper she completes.
s = stickers earned
p = papers completed
The independent variable is:
s = stickers earned
p = papers completed
Zach and his friends are at an arcade and are redeeming their tickets for prizes. The number of prizes they can get is calculated based on how many tickets they have won.
p = the number of prizes the friends can get
t = the number of tickets the friends have won
t is the independent variable and p is the dependent variable
p is the independent variable and t is the dependent variable
Belle manages the Hancock Orchard, which produces many different types of fruit, including pears. The more pear trees that have been planted in the orchard, the more barrels of pears the orchard will produce.
p = the number of pear trees that have been planted in the orchard
b = the number of barrels of pears the orchard will produce
p is the independent variable and b is the dependent
b is the independent variable and p is the dependent
A school committee is assigned the task of selecting a DJ for their annual dance night. They were able to find a DJ who charges 5000 pesos for every 3 hours. How much will the school pay if the dance lasts for 9 hours? (use the word pesos in small letter as unit of measure, (a) pesos)
The distance covered by a moving object with a constant rate varies directly as the time it travelled. Milo walked 40 meters in 15 seconds. How long will it take him to walk 128 meters with a constant rate? (use small letter for the unit of measure, (a) seconds)
An equation of direct variation can be written in the form: y = kx
True
False
The letter k in the equation y = kx stands for
the constant of proportionality
king
queen
Do x and y show direct variation?
y = 2x + 3
Yes
No
Do x and y show direct variation?
y = 5x
Yes
No
Do x and y show direct variation?
y = x2
Yes
No
The graph of a direct variation must be a straight line and must pass though
Quadrant 1 and 3
Quadrant 2 and 4
the origin (0,0)
Is this the graph of a direct variation?
Yes
No
Is this the graph of a direct variation?
Yes
No
Does this table of values represent a direct variation?
Yes
No
Does this represent a direct variation?
Yes
No
Which of the following 2 graphs represents a direct variation relationship?
Which of the following equations represents a direct variation relationship with a constant of proportionality(k) of 3?
y=x3
y=3x+2
y=3x
y=2x
What is the constant of proportionality (k) for the equation.
y=5x
1/5
5
.5
-5
If x is directly proportional to y, and x = 32 when y = 16, what is x when y = 9?
18
2
2/9
4
Does the following graph represent a direct variation relationship? (Make sure to read the reason to pick the best answer.)
Yes. It is a straight line.
No. Even though it is a straight line, it does not go through the origin.
Yes, it has a negative slope.
No, It goes through the origin and is a straight line.
Is this the graph of a direct variation?
Yes
No
Do x and y show direct variation?
y = x2
Yes
No
Do x and y show direct variation?
y = 5x
Yes
No
Do x and y show direct variation?
y = 2x + 3
Yes
No
An equation of direct variation can be written in the form: y = kx
True
False
The value of y is directly proportional to the value of x. When x=512, y = 128. What is the value of y when x=64?
256
32
16
8
The value of y is directly proportional to the value of x. If x=3 then y=21. What is the value of x when y=105?
0.6
1.67
7
15
