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Name
Date
Function Families for 200, Alex…
Recognizing Functions by Characteristics
Problem Set
Choose the appropriate function family or families to complete each sentence based on the given
characteristic(s).
linear functions
exponential functions
quadratic functions
linear absolute value functions
1. The graph of this function family is a straight line. The function family is
linear functions
.
2. The graph of this function family has an increasing interval and a decreasing interval. The function
family is
.
3. The graph of this function family has an absolute minimum. The function family is
.
4. The graph of this function family in decreasing over the entire domain. The function family is
.
5. The graph of this function family forms a V shape. The function family is
.
© 2012 Carnegie Learning
6. The graph of this function family has an increasing interval and a decreasing interval and forms
a U shape. The function family is
.
7. The graph of this function family does not have an absolute maximum or absolute minimum and
is a smooth curve. The function family is
.
8. The graph of this function family has an absolute maximum or absolute minimum and is made up
straight lines. The function family is
.
9. The graph of this function family is made up straight lines and does not have an absolute maximum
or absolute minimum. The function family is
.
10. The graph of this function family decreases over the entire domain and is a smooth curve.
The function family is
.
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Create an equation and sketch a graph for a function with each set of given characteristics. Use values
that are any real numbers between 210 and 10.
11. Create an equation and sketch a graph that:
r is a smooth curve,
r is continuous,
r has a minimum, and
r is quadratic.
Answers will vary.
y
f(x) 5 x2
8
6
4
2
0 2
28 26 24 22
22
4
6
8
x
24
26
28
12. Create an equation and sketch a graph that:
r is linear,
r is discrete, and
© 2012 Carnegie Learning
r is decreasing across the entire domain.
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page 3
Date
13. Create an equation and sketch a graph that:
r is a smooth curve,
r is increasing across the entire domain,
r is continuous, and
r is exponential.
14. Create an equation and sketch a graph that:
r has a maximum,
r is continuous, and
© 2012 Carnegie Learning
r is a linear absolute value function.
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15. Create an equation and sketch a graph that:
r is linear,
r is continuous,
r is neither increasing nor decreasing across the entire domain, and
r does not pass through the origin.
16. Create an equation and sketch a graph that:
r is discrete,
r has a maximum,
r does not pass through the origin, and
© 2012 Carnegie Learning
r is quadratic.
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LESSON 1.4
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page 5
Name
Date
Choose the function family represented by each graph.
linear function
linear absolute value function
quadratic function
linear piecewise function
17.
exponential function
18.
y
y
8
8
6
6
4
4
2
2
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4
6
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x
0 2
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28
4
6
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4
6
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x
The graph represents a quadratic function.
19.
20.
© 2012 Carnegie Learning
y
y
8
8
6
6
4
4
2
2
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22
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6
8
x
0 2
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24
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x
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page 6
22.
y
y
8
8
6
6
4
4
2
2
0 2
28 26 24 22
22
4
6
8
x
0 2
28 26 24 22
22
24
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6
8
x
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