The range of a function is the collection of numbers (or set) containing all the function's outputs.
Consider the function defined by the mapping diagram below.
In a mapping diagram, the range consists of all the outputs to which an arrow is drawn. Therefore, the range is
The value is not part of the range because there is no -value such that
What is the range of the function defined by the mapping diagram shown below?
The range of consists of all the outputs that have a corresponding -input.
In a mapping diagram, the range consists of all the outputs to which an arrow is drawn.
Therefore, the range is the set
What is the range of the function $g$ defined by the mapping diagram shown above?
|
a
|
$(2,10]$ |
|
b
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$\{ 4,6,8,10 \}$ |
|
c
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$\{ 0,4,6,8,10 \}$ |
|
d
|
$ [4,10]$ |
|
e
|
$(-\infty,\infty)$ |
What is the range of the function $f$ defined by the mapping diagram shown above?
|
a
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$[1, 4]$ |
|
b
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$[0,4]$ |
|
c
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$ \{0, 2, 1, 4 \}$ |
|
d
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$[1, \infty]$ |
|
e
|
$ \{1, 2, 4 \}$ |
What is the range of the function defined by the following table?
The range of consists of all the outputs that have a corresponding -input.
In a table, the range consists of all numbers that feature in the row corresponding to
Therefore, the range is the set
What is the range of the function $f$ defined by the following table?
| $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
| $f(x)$ | $0$ | $-3$ | $1$ | $2$ | $-1$ | $4$ |
|
a
|
$\{0,1,2,4 \}$ |
|
b
|
$\{-3,-1,0,1,2,4 \}$ |
|
c
|
$[-3,4]$ |
|
d
|
$[-3,2]$ |
|
e
|
$\{-3,-2,-1,0,1,2 \}$ |
What is the range of the function $h$ defined by the following table?
| $x$ | $0$ | $1$ | $-2$ | $3$ | $-4$ | $5$ | $-6$ | $7$ |
| $h(x)$ | $-7$ | $6$ | $-5$ | $4$ | $-3$ | $6$ | $-1$ | $0$ |
|
a
|
$( -7, 0 )$ |
|
b
|
$[ -7, 6 ]$ |
|
c
|
$\{ -7, -5, -3, -1, 0, 4, 6 \}$ |
|
d
|
$\{ -7, 0 \}$ |
|
e
|
$\{ -7, -5, -3, -1, 0, 2, 4, 6 \}$ |
When we graph a function, the range is the set of all -values given by the graph.
For example, consider the linear function graphed below.
The graph covers all -values, so the range of the function is
which we can also write as
Furthermore, we can express the range as using interval notation.
If we restrict the domain, the range also changes. Let's now consider the function
The graph is shown below.
The values go from up to (but not including) including every value in between. Therefore, the range of the function is
Using interval notation, we can also write the range as
What is the range of the function defined by the graph below?
First, we find the lowest and highest -values in the graph.
The lowest -value is This occurs at the point
The highest -value is This occurs at the point
The function covers all the -values between and including both and
Therefore, the range is
which can also be written as
What is the range of the function $f(x),$ shown above?
|
a
|
$-1 \leq f(x)\leq 1$ |
|
b
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$-4 \lt f(x)\lt 4$ |
|
c
|
$-4 \leq f(x)\leq 4$ |
|
d
|
$-1 \leq f(x)\leq 0$ |
|
e
|
$-1 \leq f(x)\lt 1$ |
What is the range of the function $f(x),$ shown above?
|
a
|
$-1 \lt f(x) \lt 3$ |
|
b
|
$-1 \leq f(x) \leq 3$ |
|
c
|
$-3 \leq f(x) \leq 1$ |
|
d
|
$0 \lt f(x) \leq 3$ |
|
e
|
$-3 \lt f(x) \lt 1$ |