Name: _________________________________
Date: ____________
Linear, Quadratic, and Exponential Functions Inventory Probe
I am not comfortable with
this and need additional
help.
I am comfortable with this
and can explain it to
others.
Circle the number (1-5) that describes how comfortable you are with the concepts discussed in this
module.
Determine a linear function from a table
or a graph.
1
2
3
4
5
Determine a quadratic function from a
table or a graph.
1
2
3
4
5
Determine an exponential function from
a table or a graph.
1
2
3
4
5
Formulate linear, quadratic and
exponential functions that model
real-world situations.
1
2
3
4
5
Analyze functions.
1
2
3
4
5
Describe the rate of change for a
function.
1
2
3
4
5
Determine the domain and range of
linear, quadratic, and exponential
functions.
1
2
3
4
5
Describe and locate on a graph the key
attributes of linear functions.
1
2
3
4
5
Describe and locate on a graph the key
attributes of quadratic functions.
1
2
3
4
5
Describe and locate on a graph the key
attributes of exponential functions.
1
2
3
4
5
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
Date: ____________
Linear, Quadratic, and Exponential Functions
For each box attach a Function Card that represents the named function. Determine the value(s)
for the named attribute of the graph.
Linear Function
Domain:______________________
Quadratic Function
x-intercept(s):______________________
Accelerated Intervention, Algebra 1
Linear Function
Slope:______________________
Quadratic Function
Axis of symmetry:__________________
© Region 4 Education Service Center
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Name: _________________________________
Date: ____________
Exponential Function
Exponential Function
Asymptote:______________________
Range:______________________
Attach the two remaining cards. Determine the type of function it is, and determine one of
the attributes of each graph.
_____________ Function
___________ Function
______________________
______________________
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Function Cards
Cut along the dotted lines
A
C
x
f(x)
–2
–6
–1
–9
0
–12
1
–15
2
–18
x
f(x)
0
1
1
3
2
9
3
27
4
81
E
B
A colony of 125 bacteria triples
every hour. The number of bacteria
in the colony is a function of the
number of hours.
D
Each week Mayette deposits $25
into her no-interest bank account.
The balance of her account is a
function of the number of deposits.
F
3
f (x) = − x2 + 3
2
G
H
x − 3y = 15
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
Date: ____________
Linear, Quadratic, or Exponential?
Match each of the Linear, Quadratic, or Exponential Cards to the appropriate function. Attach
each card in the appropriate column, and write one additional statement to describe each function.
Linear Functions
Accelerated Intervention, Algebra 1
Quadratic Functions
Exponential Functions
© Region 4 Education Service Center
All rights reserved.
Linear, Quadratic, or Exponential? Cards
Cut along the dotted line.
The graph is symmetric
about a vertical line drawn
through the vertex of the
parabola. This vertical line is
called the axis of symmetry.
Can be written in the form
f ( x ) = ax 2 + bx + c.
Can have up to 2
x-intercepts.
Can be written in the form
f ( x ) = mx + b.
The graph is a straight line.
The function can model
growth or decay by a
constant factor.
The graph of the function has
an asymptote.
Can be written in the form
f (x ) = ab x .
Has a constant rate of
change.
To determine the function
value for the next
consecutive x-value, the
previous function value is
multiplied by a constant.
The vertex is either a
maximum or a minimum
value of the function.
The independent variable is
in the exponent.
To determine the function
value for the next
consecutive x-value, a
constant is added to the
previous function.
The function either is
increasing to a point then is
decreasing or is decreasing to
a point then increasing.
The polynomial has a degree
of 1.
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
Date: ____________
Assess: Types of Functions
1
The table represents some points on the graph of quadratic function f.
x
f(x)
–2
5
–1
0
0
–3
1
–4
2
–3
3
0
What is the range of f?
2
A
f (x) ≥ − 1
B
f ( x ) ≤ −3
C
f ( x ) ≥ −4
D
f (x) ≤ 5
Scientists are tracking the population of a specific species of bird. They have determined that
the function P(x) = 575(1.025)x models the number of birds, P(x), in thousands after x years.
Which of the following is true about the bird population?
A
The number of birds was initially 1,025 birds.
B
The number of birds was initially 575 birds.
C
The number of birds of birds is increasing by 25% each year
D The number of birds of birds is decreasing by 2.5% each year
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
3
4
Date: ____________
The population of Midsize City, USA is 150,000 and is expected to grow 5% each year. Which of
the following functions best represents the population after x years?
A
f (x) = 5(150, 000)
B
f (x) = 150, 000(5)
C
f (x) = 0.05(150, 000)
D
f (x) = 150, 000(1.05)
x
x
x
x
A table of values for the linear function g is shown below.
x
g(x)
10
17.50
15
23.75
24
35.00
28
40.00
30
42.50
Which situation can be modeled by this function?
A
The cost of a taxi ride is $1.25 per mile plus a $5.00 surcharge.
B
The cost of a taxi ride is $1.50 per mile plus a $5.00 surcharge.
C
The cost of a taxi ride is $1.25 per mile plus a $2.50 surcharge.
D The cost of a taxi ride is $1.50 per mile plus a $2.50 surcharge.
5
The function y = –50x + 475 can be used to find the amount of money in Antwann’s savings
account x months after he opens the account. Based on this information, which statement
about the graph of this situation is true?
A
The y-intercept of the graph represents the amount being withdrawn each month.
B
The slope of the graph represents the amount being withdrawn each month.
C
The x-intercept of the graph represents the initial deposit amount.
D The slope of the graph represents the initial deposit.
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
6
Date: ____________
The graph shows the number of miles Dan is from home based on the time he spent driving.
Distance from Home, miles
Dan’s Drive Home
Time Spent Driving, hours
Based on the information in the graph, what is a reasonable domain for this situation?
7
A
All real numbers
B
0≤ x ≤5
C
0 ≤ x ≤ 350
D
x ≤5
A rocket is launched from the ground. The height of the rocket at time x can be modeled by the
equation f ( x ) = −16 x 2 + 180 x. Based on this function, which statement is true?
A
The height of the rocket will reach a maximum between 5 and 6 seconds.
B
The height of the rocket will decrease and then increase.
C
The height of the rocket is increasing at a constant rate.
D The height of the rocket reaches 164 meters two seconds after launch.
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
8
9
Date: ____________
Which of the following graphs best represents exponential decay?
A
C
B
D
Which of the following does not describe the graph of the function f ( x ) = −4 x 2 + 2 x + 6 ?
A
The points (‒1, 0) and (1.5, 0) are x-intercepts of the graph of the function.
B
The vertex of the function occurs at the point (0.25, 6.25).
C
The axis of symmetry of the function is x = 6.25.
D The graph of the function has a maximum.
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.
Name: _________________________________
Date: ____________
10 The graph below shows the population growth for a particular type of bacteria over several
hours.
Population (in thousands)
Bacteria Growth
Time (in hours)
Based on the information in the graph, what is a reasonable prediction for the bacteria
population after 6 hours?
A
90,000
B
243,000
C
729,000
D 2,187,000
Accelerated Intervention, Algebra 1
© Region 4 Education Service Center
All rights reserved.