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To determine the domain and range of the relationship shown in the graph, we can identify the minimum and maximum $x-$ and $y-$values the graph covers. We will recreate the graph, placing points on the minimum and maximum points for $x$ and $y.$

By looking at the highlighted points on the graph we can write the minimum and maximum values for $x$ and $y.$
$Minimum value ofx:Maximum value ofx:Minimum value ofy:Maximum value ofy: -3-3-3-3 $
Using the above, we can write the domain and range of the relationship. $Domain:Range: -3≤x≤3-3≤y≤3 $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. Consider the points we have highlighted earlier.
$(-3,0),(0,3),(3,0),(0,-3) $
We can see that for the input $0$ there are two outputs, $3$ and $-3.$ Therefore, this relationship is **not** a function.

b

The arrows indicate that the line continues to the left and downwards, and to the right and upwards. This means that all $x-$values are possible inputs and all $y-$values are possible outputs.
$Domain:Range: All real numbers.All real numbers. $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. From the graph we can see that for each $x-$value there is exactly one corresponding $y-$value. Therefore, this relationship is a function.

c

By looking at the highlighted points on the graph we can write the minimum and maximum values for $x$ and $y.$
$Minimum value ofx:Maximum value ofx:Minimum value ofy:Maximum value ofy: -2-4-4-2 $
Therefore, we can write the domain and range of the relationship. $Domain:Range: -2≤x≤4-4≤y≤2 $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. From the graph we can see that for each $x-$value there is exactly one corresponding $y-$value. Therefore, this relationship is a function.

d

To determine the domain and range, let's take a look at the given graph. We will highlight the maximum point of the graph.

The maximum value of $y$ is $4.$ The arrows indicate that the graph continues downwards. This means that all $y-$values *less than or equal to* $4$ are possible outputs. Since there are no restrictions, all $x-$values are possible inputs. Let's write the domain and range of the relationship.
$Domain:Range: All real numbers.y≤4 $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. From the graph we can see that for each $x-$value there is exactly one corresponding $y-$value. Therefore, this relationship is a function.

e

To determine the domain and range of the relationship shown in the graph, we can identify the minimum and maximum $x-$ and $y-$values the graph covers. We will recreate the graph, placing points on the minimum and maximum points for $x$ and $y.$

By looking at the highlighted points on the graph we can write the minimum and maximum values for $x$ and $y.$
$Minimum value ofx:Maximum value ofx:Minimum value ofy:Maximum value ofy: -2-4-3-2 $
Therefore, we can write the domain and range of the relationship. $Domain:Range: 2≤x≤4-3≤y≤2 $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. Consider the points we have highlighted earlier.
$(4,-3),(2,-1),(4,1),(3,2) $
We can see that for the input $4$ there are two outputs, $-3$ and $1.$ Therefore, this relationship is **not** a function.

f

To determine the domain and range, let's take a look at the given graph. We will highlight the minimum points for $x$ and $y.$ Note that in this case we only need to highlight one point.

The minimum value of $x$ is $0$ and the minimum value of $y$ is $3.$ The arrow indicates that the graph continues to the right and upwards. This means that all $x-$values *greater than or equal to* $0$ are possible inputs, and all $y-$values *greater than or equal to* $3$ are possible outputs.
$Domain:Range: x≥0y≥3 $
Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x-$value, there is __exactly one__ output, or $y-$value. From the graph we can see that for each $x-$value there is exactly one corresponding $y-$value. Therefore, this relationship is a function.