WorksheetsUnit 4 Non-Linear Functions
Total questions: 116
Worksheet time: 3hrs 9mins
Name
Class
Date
1.
What is the vertex of the graph?
a)
(2,4)
b)
(-2,-4)
c)
(4,2)
d)
(-4,-2)
2.
Over what interval is the function increasing?
a)
x < -3
b)
x > -3
c)
y < -10
d)
y > -10
3.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
4.
What are the x-intercepts of the graph?
a)
(-1,0) and (0,6)
b)
(3,0) and (0,6)
c)
(-1,0) and (3,0)
d)
(0,-1) and (0,3)
5.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
6.
What is the y-intercept?
a)
(3,0)
b)
(0,-3)
c)
(0,3)
d)
(-3,0)
7.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
8.
What is the domain?
a)
y < 4
b)
1 < x < 5
c)
x > 0
d)
All real numbers
9.
What is the range?
a)
y < 4
b)
y > 4
c)
x < 4
d)
All real numbers
10.
In the calculator, find the vertex of
f(x) = -x2 - 4x + 12. Is it a max or min?
f(x) = -x2 - 4x + 12. Is it a max or min?
a)
(-2, 16), minimum
b)
(-2, 16), maximum
c)
(0, 12), minimum
d)
(0, 12), maximum
11.
Which equation below is a quadratic?
a)
y=9x+5
b)
y=3x2 - 6
c)
y=5x3+6
d)
x=3x
12.
(calculator) A ball thrown follows
y= -0.88x2+11x+3 where x=time and y=height. When did it reach it's max height?
y= -0.88x2+11x+3 where x=time and y=height. When did it reach it's max height?
a)
37.375 feet
b)
37.375 seconds
c)
6.25 feet
d)
6.25 seconds
13.
What is the y-intercept of
f(x)=2x2 + 4x + 6 (Hint: use [2nd] [GRAPH] or just plug in 0)
f(x)=2x2 + 4x + 6 (Hint: use [2nd] [GRAPH] or just plug in 0)
a)
(6 , 0)
b)
(-6 , 0)
c)
(0, -6)
d)
(0 , 6)
14.
If each mark on the x-axis represents one second, when did the object reach its maximum height?
a)
2.5 seconds
b)
2 seconds
c)
5.5 seconds
d)
3 seconds
15.
If each mark on the x-axis represents one second, when did the object reach the ground?
a)
2.5 seconds
b)
6 seconds
c)
5.5 seconds
d)
5 seconds
16.
A rocket follows f(x) = -x2 - 4x + 12 where x=minutes & f(x)=meters. When did the rocket land? (calculator)
a)
after 5.2 minutes
b)
5.2 meters away
c)
after 2 minutes
d)
20 meters away
17.
Does
y = -4x2
have a maximum or minimum value?
y = -4x2
have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
18.
#9) A raft is dropped from a helicopter 256 feet in the air above the ocean. Its approximate height, h, after t seconds is given by the function h(t) = -16t2 + 256. How many seconds did it take the raft to hit the water?
a)
-4
b)
2
c)
4
d)
8
19.
Over what interval is this function constant?
a)
x < -3
b)
-3 < x < 4
c)
x > 4
d)
-5
20.
When is this function increasing?
a)
-2.5 < x < 2.5
b)
0 < x < 5
c)
0 < x < 55
d)
-5 < x < 0
21.
How long did Sam sit on the bench and wait for the bus?
a)
5 min
b)
10 min
c)
15 min
d)
20 min
22.
Over which interval of time is this person returning home?
a)
8:00 < x < 9:00
b)
9:00 < x < 9:30
c)
9:30 < x < 11:00
d)
12:00 < x < 13:00
23.
Interpret the meaning of the coordinate
(12.00, 5).
(12.00, 5).
a)
At 5 o'clock the kayak had traveled 12.0 km.
b)
At 12 o'clock they were going 5 km/hr.
c)
At 12 o'clock the kayak had traveled 5 km.
d)
At 5 o'clock they were going 12.0 km/hr
24.
On what interval is the function increasing?
a)
y ≤ 1
b)
y ≥ 1
c)
x ≥ -2
d)
x ≤ -2
25.
Where is the function decreasing?
a)
x ≤ 1
b)
x ≥ 1
c)
x ≤ -1
d)
-1 < x < 3
26.
Where is the function increasing?
a)
nowhere
b)
x < -1
c)
x > -1
d)
y ≤ 3
27.
Where is the function increasing?
a)
y≥4
b)
y≤4
c)
y≥-4
d)
y≤-4
28.
Identify the slope, intercepts, and whether the line is increasing or decreasing.
a)
Slope = -2
X-intercept = (2, 0)
Y-intercept = (0, 4)
Decreasing
X-intercept = (2, 0)
Y-intercept = (0, 4)
Decreasing
b)
Slope = -½
X-intercept = (0, 2)
Y-intercept = (4, 0)
Decreasing
X-intercept = (0, 2)
Y-intercept = (4, 0)
Decreasing
c)
Slope = -2
X-intercept = (0, 2)
Y-intercept = (4, 0)
Decreasing
X-intercept = (0, 2)
Y-intercept = (4, 0)
Decreasing
d)
Slope = -½
X-intercept = (2, 0)
Y-intercept = (0, 4)
Decreasing
X-intercept = (2, 0)
Y-intercept = (0, 4)
Decreasing
29.
Identify the slope, y-intercept, and whether the line is increasing or decreasing.
a)
Slope = 2
Y-int = (0, -2/3)
Increasing
Y-int = (0, -2/3)
Increasing
b)
Slope = -2/3
Y-int = (2, 0)
Decreasing
Y-int = (2, 0)
Decreasing
c)
Slope = -2/3
Y-int = (0, 2)
Decreasing
Y-int = (0, 2)
Decreasing
d)
Slope = -2/3
Y-int = (2, 0)
Decreasing
Y-int = (2, 0)
Decreasing
30.
Calculate the average rate of change between the following points.
(3, -1) and (-5, 4)
(3, -1) and (-5, 4)
a)
-8/5
b)
-5/8
c)
3/2
d)
-3/2
31.
f(x)=x2-2x+1
Evaluate the function for f(-1).
Evaluate the function for f(-1).
a)
f(-1)=4
b)
f(-1)=0
c)
f(-1)=2
d)
f(-1)=-1
32.
f(x)=2x+1
If f(x)=4, what is the value of x?
If f(x)=4, what is the value of x?
a)
3/2
b)
2
c)
1/2
d)
4
33.
f(x)=x2-2x+1
What is the "name" of the function?
What is the "name" of the function?
a)
g
b)
x
c)
f
34.
Which ordered pair could represent a y-intercept on a graph?
a)
(6, 0)
b)
(0, 4)
c)
(-1, 3)
d)
(2, 0)
35.
Which ordered pair could represent an x-intercept on a graph?
a)
(0, 5)
b)
(-1, 2)
c)
(4, 0)
d)
(2, 1)
36.
Determine if the graph is linear, exponential or quadratic. How do you know?
a)
Exponential; it decreases then increases
b)
Quadratic; it decreases then increases
c)
Linear; it is curvy
d)
Exponential; it increases slowly
37.
Determine if the graph is linear, quadratic, or exponential. Describe the rate of change.
a)
Linear; the rate of change is the same (constant)
b)
Linear; the rate of change gets bigger as x increases
c)
Quadratic; the rate of change is negative then positive
d)
Exponential; the rate of change is always positive
38.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(1 - 0.30)x
b)
y=0.30(5000)x
c)
y=5000(1 + 0.30)x
d)
y=5000x0.30
39.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1 + 14)x
c)
y=6(1 + 0.14)x
d)
y=6(1 - 0.14)x
40.
In an exponential function, what does the 'a' represent?
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO (What is being multiplied repeatedly)
41.
g(x)=3(2)x
Find g(3)
Find g(3)
a)
216
b)
24
c)
18
d)
28
42.
Des Moines is having a blizzard. It has already snowed 1 inch and the total will double each hour. Write an equation.
a)
y=1(2)x
b)
y=1(1/2)x
c)
y=2(1/2)x
d)
y=2(2)x
43.
Your shiny new boat cost $7650. The depreciation(how it loses value) for your boat is 14% per year. Estimate the value of your vehicle in 3 years. How would you calculate the answer?
a)
y= 7650(0.14)3
b)
y= 7650(1 - 0.14)3
c)
y= 7650(1+0.14)3
d)
y= -14(3) + 7650
44.
A new savings account is opened with $400 and gains 3% every year. What is the exponential function?
a)
f(x)=400(1+3)x
b)
f(x)=400(1+ 0.3)x
c)
f(x)=400(1+0.03)x
d)
f(x)=400(0.03)x
45.
The value of a car is $15,000 and depreciates (loses value) at a rate of 8% per year. What is the exponential equation?
a)
y=8(15,000)x
b)
y=15,000(1.8)x
c)
y=15,000(1 - 0.08)x
d)
y=15,000(0.08)x
46.
What type of function is
f(x) = 2(1/7)x ?
How do you know?
f(x) = 2(1/7)x ?
How do you know?
a)
Exponential Growth; b > 1
b)
Quadratic; it has an exponent
c)
Exponential Decay; b < 1
d)
Quadratic; a > 1
47.
What is the y-intercept of the function?
a)
(0,2)
b)
(0,3)
c)
(3,0)
d)
(-6,0)
48.
Given y=3x determine the y-intercept
a)
(0,1)
b)
(0,3)
c)
There isn't one
49.
Is this exponential growth or decay?
a)
Growth
b)
Decay
50.
Is the graph linear, exponential, quadratic, or neither?
a)
Linear
b)
Exponential
c)
Quadratic
d)
Neither
51.
Is the pictured graph exponential growth or decay?
a)
Exponential
Decay
Decay
b)
Exponential
Growth
Growth
52.
What is the initial amount for the function:
f(x) = 300(1.16)x?
f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
348
53.
Convert 3% to a decimal
a)
3
b)
.3
c)
.03
d)
.003
54.
In an exponential function, what does the 'b' represent?
a)
SLOPE
b)
RATE OF CHANGE
c)
STARTING VALUE
d)
GROWTH FACTOR
55.
What is the pattern you see in this table?
a)
Multiplying by 1/3
b)
Adding 8
c)
Multiplying by 3
d)
Dividing by 3
56.
Which equation matches the graph?
a)
y=2(2)x
b)
y=2(½)x
c)
y=2x
d)
y=½(2)x
57.
Change 6.75% to a decimal.
a)
67.5
b)
.675
c)
675
d)
.0675
58.
Which equation matches the graph?
a)
y = 2(1)x
b)
y = (½)x
c)
y = 2x
d)
y = 2(½)x
59.
What is the y-intercept of the line?
a)
(0,1/2)
b)
(0,1)
c)
(0, -1/2)
d)
(0, -1)
60.
What is the y-intercept?
a)
(0,7)
b)
(-2,3)
c)
(8,0)
d)
(1,9)
61.
Write the equation:
a)
y = -½x + 4
b)
y = 2x - 4
c)
y = -2 + 4
d)
y = -2x + 4
62.
Write the Equation:
a)
y = 3/2x - 2
b)
y = 3/2x + 3
c)
y = 2/3x - 2
d)
y = 2/3x + 3
63.
The slope of this line is...
a)
Positive
b)
Negative
c)
Zero
d)
Undefined
64.
A graph is linear if it:
a)
travels in a straight line
b)
curves
c)
is u-shaped
d)
is boomerang-shaped
65.
The slope is defined as the:
a)
y intercept
b)
run of the graph
c)
rise of the graph
d)
rate of change
66.
What is coordinate L?
a)
(6,6)
b)
(2,5)
c)
(2,3)
d)
(5,2)
67.
The height of an object is represented by the function h(t) = 300 - 19t2, where 300 represents the initial height in feet and t represents the elapsed time in seconds. About how many seconds will it take for the object to hit the ground? (use your calculator)
a)
-4 seconds
b)
4 seconds
c)
300 seconds
d)
-19 seconds
68.
On the graph shown, one of the zeros is located between which of the following integers?
a)
Between -2 and -3
b)
Between 2 and 3
c)
Between 5 and 6
d)
It's at (2,4)
69.
If the y-axis represents profit, and the x- axis represents selling price, how much should this company sell their product for to maximize profit?
a)
$55,000
b)
$50
c)
$100
d)
$200
70.
Does this parabola have a minimum or maximum and WHAT is its value?
a)
minimum: 2
b)
maximum: 2
c)
minimum: 5
d)
maximum: 5
71.
The graph below shows the height of a baseball from the time it is thrown from the top of a building to the time it hits the ground. From the graph, what conclusion can be made about the flight of the baseball?
a)
A.The baseball reached its maximum height after 4.5 seconds.
b)
The baseball was 120 meters or more above the ground over 3 < x < 5.
c)
At 2 seconds, the height of the baseball was 95 meters.
d)
The baseball was in flight for 8 seconds.
72.
The graph below shows h, the height in meters of a model rocket, versus t, the time in seconds after the rocket is launched. From the graph, what conclusion can be made about the flight of the rocket?
a)
The height of the rocket was 14 meters at 3 seconds.
b)
The rocket reached its maximum height after 2 seconds.
c)
The height of the rocket was 0 meters when it was launched.
d)
The height of the rocket was more than 15 meters for t > 1.5.
73.
Which runner won the 10m race?
a)
A
b)
B
c)
C
74.
What is the average rate of change from hour 3 to hour 5?
a)
1 miles per hour
b)
50 miles per hour
c)
25 miles per hour
d)
37.5 miles per hour
75.
Which statement below accurately represents the graph?
a)
$100 is earned for each hour worked
b)
$100 is earned for every 2 hours worked
c)
$500 is earned for every 8 hours worked
d)
$200 is earned for every 4 hours worked
76.
At what rate did the rain fall?
a)
2 cm per hour
b)
1/4 cm per hour
c)
1/2 cm per hour
d)
4 cm per hour
77.
f(x) = 3(2)x
What is the average rate of change of f(x) on the interval 1 ≤ x ≤ 4?
What is the average rate of change of f(x) on the interval 1 ≤ x ≤ 4?
a)
430
b)
14
c)
42
d)
45
78.
f(x) = 4x+5
What is the average rate of change of f(x) over the interval
2 ≤ x ≤ 3
What is the average rate of change of f(x) over the interval
2 ≤ x ≤ 3
a)
48
b)
24
c)
-48
d)
-24
79.
Which of the following are ways to find the rate of change?
a)
change in y over change in x
b)
rise over run
c)
(y2-y1) over (x2-x1)
d)
all of the above
80.
What is the average rate of change from x= -1 and x=0?
a)
-2
b)
-1/2
c)
2
d)
1/2
81.
Use the table below to find the average rate of change from x=2 to x=4.
a)
12
b)
-12
c)
-6
d)
6
82.
Does the table represent a linear, quadratic, or exponential function?
a)
Linear
b)
quadratic
c)
exponential
83.
Does the table represent a linear, quadratic, or exponential function?
a)
linear
b)
quadratic
c)
exponential
84.
Is the table linear, quadratic, exponential, or neither?
a)
Linear
b)
Quadratic
c)
Exponential
d)
Neither
85.
Is the graph linear, quadratic, exponential, or neither?
a)
Linear
b)
Quadratic
c)
Exponential
d)
Neither
86.
Is the equation linear, exponential, or quadratic?
y = 2x+ 4
y = 2x+ 4
a)
Linear
b)
Exponential
c)
Quadratic
d)
None of the above
87.
What type of function best models the situation: A zombie virus has infected the population and the number of infected people triples every day.
a)
linear
b)
quadratic
c)
exponential growth
d)
exponential decay
88.
What rate of change is faster/larger?
a)
Linear
b)
Exponential
c)
Quadratic
d)
Absolute Value
89.
Which function is a larger function as x gets larger?
a)
y = a (b)x
b)
y = x2
c)
y = mx+b
90.
With x being time and y being height, how much time does it take for the ball to get to max height?
a)
At 1 second
b)
At 2 seconds
c)
At 3 seconds
d)
At 4 seconds
91.
The change in the height of a ball from one bounce to the next is 75% of its previous height. Which of the following is true?
a)
This is an example of exponential growth with the growth factor being 1.75.
b)
This is an example of exponential decay with the decay factor being .75.
c)
This is an example of linear growth with the rate of change being .75.
d)
This is an example of linear decay with the rate of change being -.75.
92.
A taxi company charges a flat rate of $3.50 plus $0.20 for each additional mile. Which of the following is true?
a)
This is an example of exponential growth with the model being y = 3.5(1.20)x
b)
This is an example of exponential decay with the model being y = 3.5(.20)x
c)
This is an example of linear growth with the model being
y = .20x + 3.50
y = .20x + 3.50
d)
This is an example of linear decay with the model being
y = -.20x + 3.50
y = -.20x + 3.50
93.
a)
The rate of change of the function f(x) is always greater than the rate of change of the function g(x)
b)
The rate of change of the function g(x) will eventually be greater than the rate of change of the function f(x)
c)
The rate of change of the function f(x) is never greater than the rate of change of the function g(x)
d)
The rate of change of the function g(x) is never greater than the rate of change of the function f(x)
94.
Identify the function shown
.
.
a)
Linear
b)
Quadratic
c)
Exponential
d)
Not answering
95.
Identify the function shown
.
.
a)
Linear
b)
Quadratic
c)
Exponential
d)
No Clue
96.
Identify the function shown
.
.
a)
Linear
b)
Quadratic
c)
Exponential
d)
#dontevenknow
97.
Which function is represented by the following equation.
y = 5x2-4x+10
y = 5x2-4x+10
a)
Linear
b)
Quadratic
c)
Exponential
d)
IDK
98.
Which function is represented by the following equation.
y = 3x
y = 3x
a)
Linear
b)
Quadratic
c)
Exponential
d)
IDK
99.
Which function is represented by the following equation.
y = -3x+8
y = -3x+8
a)
Linear
b)
Quadratic
c)
Exponential
d)
IDK
100.
Read the word problem below and determine which function is a correct representation.
A population of 800 beetles is growing each month at a rate of 5%.
A population of 800 beetles is growing each month at a rate of 5%.
a)
Linear
b)
Quadratic
c)
Exponential
d)
IDK
101.
Read the word problem below and determine which function is a correct representation.
A local donut establishment charges 20 cents per donut. The amount charged is a function of donuts bought.
A local donut establishment charges 20 cents per donut. The amount charged is a function of donuts bought.
a)
Linear
b)
Quadratic
c)
Exponential
d)
IDK
102.
Which function has the greatest y-intercept?
a)
f(x)
b)
h(x)
c)
g(x)
103.
Which function is linear?
a)
f(x)
b)
h(x)
c)
g(x)
104.
Which function is quadratic?
a)
f(x)
b)
h(x)
c)
g(x)
105.
Which function is exponential?
a)
f(x)
b)
h(x)
c)
g(x)
106.
Which function is greater over the interval -1 <x < 1?
a)
f(x)
b)
h(x)
c)
g(x)
107.
Which function is greater over the interval x < -1?
a)
f(x)
b)
h(x)
c)
g(x)
108.
Which function will be greater for larger values of x?
a)
f(x)
b)
h(x)
c)
g(x)
109.
Jame's 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.
a)
70(2)35
b)
70(2)5
c)
2(70)5
d)
5(70)2
110.
a)
A.
b)
B.
c)
C.
d)
D.
111.
What is the y-intercept of y=20(3)x
a)
(0,0)
b)
(0,1)
c)
(0,3)
d)
(0,20)
112.
You invest $400 for 5 years and the interest rate is 4.29% each year.
a)
y=400(0.0429)5
b)
y=400(1.0429)5
c)
y=400(4.29)5
d)
y=400(4.29)(5)
113.
When a basketball is shot, it forms an arc (also known as a parabola). When the basketball reaches it's highest point, what is that point called?
a)
Minimum value
b)
Slope
c)
Maximum value
d)
A parabola
114.
Joe Mauer hits a fly ball. You can track the height of the ball using the equation:
h(t) = -16t2 + 140t + 2
What was the starting
height of the ball?
h(t) = -16t2 + 140t + 2
What was the starting
height of the ball?
a)
-16 feet
b)
140 feet
c)
2 feet
d)
0 feet
115.
Find the vertex of the quadratic:
y = -2x2 + 4x + 3
y = -2x2 + 4x + 3
a)
(0, 3)
b)
(-1, 5)
c)
(1, 5)
d)
(1, -5)
116.
320
a)
0
b)
32
c)
2.4
d)
1
100 %
