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WorksheetsUnit 3 Review Using Functions to Model Relationships
Total questions: 56
Worksheet time: 14hrs 0mins
Valerie's Gym is running a special for new members. The fee for joining the gym is $30. Members then pay $20 per month to use the gym. Identify the initial value and the rate of change of the function.
Initial Value is $20. The rate of change is $30.
Initial Value is $30. The rate of change is $20.
The rate of change and initial value are $30.
The rate of change and initial value are $20.
Valerie's Gym is running a special for new members. The fee for joining the gym is $30. Members then pay $20 per month to use the gym. Write an equation in slope-intercept form to represent this situation.
y = mx + b
y = 30x + 20
y = 20x + 30
A mechanic charges a fee of $40 to diagnose a problem, and $70 per hour for labor to fix it. Write an equation in slope intercept form to represent this situation.
y = mx + b
y = 70x + 40
y = 40x + 70
A mechanic charges a fee of $40 to diagnose a problem, and $70 per hour for labor to fix it. Identify the initial value and the rate of change.
Initial value is $40; The rate of change is $70.
The initial value is $70 and the rate of change is $40.
The rate of change is the same as the initial value $40.
The rate of change is the same as the initial value $70.
Mr. Elia picks pears at Ms. Boyle's orchard on Saturdays during the pear harvest. Ms. Boyle pays him a daily wage, plus an additional amount for each bushel of pears he picks. The table show his daily earnings, y, if he picks x bushels of pears. What is the rate of change?
10
5
8
Mr. Elia picks pears at Ms. Boyle's orchard on Saturdays during the pear harvest. Ms. Boyle pays him a daily wage, plus an additional amount for each bushel of pears he picks. The table show his daily earnings, y, if he picks x bushels of pears. What is the initial value?
25
26
29
A pool is being drained so that it can be repaired. The graph below shows the amount of water in the pool during the time it takes to drain it completely. What is the initial value?
8
6000
4
1000
A pool is being drained so that it can be repaired. The graph below shows the amount of water in the pool during the time it takes to drain it completely. What is the rate of change?
+750
-750
+6000
-1000
A pool is being drained so that it can be repaired. The graph below shows the amount of water in the pool during the time it takes to drain it completely. Write a function that is represented by the graph.
y = mx + b
y = 6000x + 750
y = -750x + 6000
y = -6000 + 750x
What are the slope and the y-intercept of the linear function that is represented by the equation
y=9x−2The slope is –2, and the y-intercept is 9.
The slope is 2, and they y-intercept is 9.
The slope is 9, and the y-intercept is –2.
The slope is 9, and the y-intercept is 2.
What are the slope and the y-intercept of the linear function that is represented by the table?
The slope is –2, and the y-intercept is 6.
The slope is –2, and the y-intercept is 12.
The slope is 2, and the y-intercept is 6.
The slope is 2, and the y-intercept is 12.
Which linear function has the greatest y-intercept?
x + 6y = 36
y = 15x + 5
3x + 8y = 24
y = 4x + 7
A daycare facility charges a fee for every minute that a parent is late after the facility’s published closing time. The table represents the fee, y, which is dependent on the number of minutes late, x. Which of the following linear equations represents the situation?
y = 6x + 2
y = 6x + 36
y = 3x + 22
y = 24x + 36
A plumber charges a $45 fee to make a house call and then $25 for each hour of labor. The plumber uses an equation in the form y = mx+b to determine the amount to charge each customer. What is the value of m in the equation?
45
25
70
20
Which is the equation of a line that has a slope of 4 and passes through point (1, 6)?
y = 4x - 2
y = 4x + 6
y = 4x + 2
y = 4x -3
Jolon used the slope-intercept form to write the equation of a line with slope 3 that passes through the point (5, –2). His work is shown above.
He forgot to add the b-value in step 5.
He added 15 to both sides in step 3.
He switched the x- and y- values in step 1.
He multiplied incorrectly in step 2.
The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.
What does the y-intercept represent?
the amount of water that is added to the barrel each day
the amount of water that remains in the water barrel
the amount that the water barrel decreases each day
the amount of water that is initially in the water barrel
The value of a collectible coin can be represented by the equation y = 2x + 9.74 , where x represents the number of years that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it?
$4.87
$ 7.74
$ 9.74
$ 19.48
Which line on the graph below has a slope of zero?
P
Q
R
S
Is the relation a function? Why?
Yes, because the x-value 11 has two y-values pair with it.
Yes, because each x-value has only one y-value paired with it.
No, because the x-value 11 has two y-values pair with it.
No, because each x-value has only one y-value paired with it.
Function
Not a Function
What is the function rule for the table?
y=3x+1
y=4x-2
y=x+1
y=x+7
Is this mapping diagram a function or not a function?
Function
Not a Function
Which set of ordered pairs represents a function?
{(3, 2), (4, 4), (6, 3), (4, 5)}
{(4, –3), (4, –1), (4, 3), (4, 6)}
{(–4, 4), (–2, 4), (1, 4), (5, 4)}
{(–3, –3), (–2, –4), (–2, –1), (–1, –5)}
The graph represents a height (y) vs. time (x) of an object. Which scenario best matches the graph?
A plane takes off, flies at a certain altitude, then lands.
A plane taxis on the run way, lifts off, ascends to a certain altitude, and flies for a while.
A plane takes off, ascends to an altitude and flies for a while, then ascends to another altitude, and flies for a while.
A plane taxis on the run way, lifts off, ascending to a certain altitude, flies for a while, ascends to a higher altitude, and flies at the new altitude.
Carly went for a walk and jog.
*She started walking.
*After a few minutes, Carly began jogging at a faster speed than she was walking.
*Carly then got tired and slowed down to a slower speed than she was jogging.
Which graph best represents the distance Carly went?
The total cost (C) for kilograms of beef (k) if each kilogram costs $2.55
The function rule for the table is y=x + 7. What are the correct ordered pairs for the table?
{(0,7), (1,-6), (2,-7), (3,-8)}
{(0,7), (1,8), (2,9), (3,10)}
{(0,7), (1,14), (2,21), (3,28)}
{(0,7), (1,8), (2,11), (3,13)}
Complete the table of values for the function y=2x
y values are (10,6,0,-6,-10)
y values are (-5,-3,0,3,5)
y values are (-10,-6,0,6,10)
y values are (-10,7,0,6,10)
What is the range of this function?
{–2, 0, 3, 5, 9}
−2≤x≤9
−3.5≤y≤7.5
{–3.5, –1.5, 1.5, 3.5, 7.5}
Find f(4) for the following function:
f(t)=–3(t–2)6
24
-6
-24
Melissa runs a graphic design business. She charges by the page, and has a setup fee. The table shows her earnings for the last few projects. What is her per-page rate?
$35 per page
$300 per page
$150 per page
$75 per page
What is the independent variable in the graph shown?
Dollars earned
Hours worked
Linear or Nonlinear
linear
nonlinear
Linear or Nonlinear
linear
nonlinear
What is the domain of a relation?
the set of all x-values
the set of all y-values
Which is the set of all y-values or the outputs?
Domain
Range
Relation
Function
What is the range of the mapping?
{1, 2, 4}
{0, 1, 2, 3}
{0, 3}
{1, 4}
{-2, 3, 7}
[-2, 7]
{1, 2, 3, 4}
[1, 4]
What is the range of the table?
{-4, 0, 1, 3}
{-2, 0, 2, 3}
{-4, -2, 0, 1, 2, 3}
{ (0, 0), (2, -4), (3, 3), (-2, 1) }
What is the domain of the relation shown in the table?
{12}
{6, 18}
{3, 9, 15, 16}
{13}
Is the relation shown a function?
No, because the x-value 11 is paired with 5 and 8.
Yes, because each x-value has only one y-value paired with it.
(3, -5) and (5, - 1)
