Describing Domain and Range

To determine the domain and range of the relationship shown in the graph, we can identify the minimum and maximum $x\text{-}$ and $y\text{-}$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 $y.$ $$\begin{array}{rlrl}\text{Minimum value of }\mathbf{x}:& \text{-}3& & \\ \text{Maximum value of }\mathbf{x}:& 3& & \\ \text{Minimum value of }\mathbf{y}:& \text{-}3& & \\ \text{Maximum value of }\mathbf{y}:& 3& & \end{array}$$ Using the above, we can write the domain and range of the relationship. $$\begin{array}{rl}\text{Domain:}& \text{-}3\le x\le 3\\ \text{Range:}& \text{-}3\le y\le 3\end{array}$$ Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x\text{-}$value, there is exactly one output, or $y\text{-}$value. Consider the points we have highlighted earlier. $$\begin{array}{c}(\text{-}3,0),(0,3),(3,0),(0,\text{-}3)\end{array}$$ We can see that for the input $0$ there are two outputs, $3$ and $\text{-}3.$ Therefore, this relationship is not a function.

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

By looking at the highlighted points on the graph we can write the minimum and maximum values for $x$ and $y.$ $$\begin{array}{rlrl}\text{Minimum value of }\mathbf{x}:& \text{-}2& & \\ \text{Maximum value of }\mathbf{x}:& 4& & \\ \text{Minimum value of }\mathbf{y}:& \text{-}4& & \\ \text{Maximum value of }\mathbf{y}:& 2& & \end{array}$$ Therefore, we can write the domain and range of the relationship. $$\begin{array}{rl}\text{Domain:}& \text{-}2\le x\le 4\\ \text{Range:}& \text{-}4\le y\le 2\end{array}$$ Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x\text{-}$value, there is exactly one output, or $y\text{-}$value. From the graph we can see that for each $x\text{-}$value there is exactly one corresponding $y\text{-}$value. Therefore, this relationship is a function.

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 $y\text{-}$values less than or equal to $4$ are possible outputs. Since there are no restrictions, all $x\text{-}$values are possible inputs. Let's write the domain and range of the relationship. $$\begin{array}{rl}\text{Domain:}& \text{All real numbers.}\\ \text{Range:}& y\le 4\end{array}$$ Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x\text{-}$value, there is exactly one output, or $y\text{-}$value. From the graph we can see that for each $x\text{-}$value there is exactly one corresponding $y\text{-}$value. Therefore, this relationship is a function.

To determine the domain and range of the relationship shown in the graph, we can identify the minimum and maximum $x\text{-}$ and $y\text{-}$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 $y.$ $$\begin{array}{rlrl}\text{Minimum value of }\mathbf{x}:& 2& & \\ \text{Maximum value of }\mathbf{x}:& 4& & \\ \text{Minimum value of }\mathbf{y}:& \text{-}3& & \\ \text{Maximum value of }\mathbf{y}:& 2& & \end{array}$$ Therefore, we can write the domain and range of the relationship. $$\begin{array}{rl}\text{Domain:}& 2\le x\le 4\\ \text{Range:}& \text{-}3\le y\le 2\end{array}$$ Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x\text{-}$value, there is exactly one output, or $y\text{-}$value. Consider the points we have highlighted earlier. $$\begin{array}{c}(4,\text{-}3),(2,\text{-}1),(4,1),(3,2)\end{array}$$ We can see that for the input $4$ there are two outputs, $\text{-}3$ and $1.$ Therefore, this relationship is not a function.

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 $x\text{-}$values greater than or equal to $0$ are possible inputs, and all $y\text{-}$values greater than or equal to $3$ are possible outputs. $$\begin{array}{rl}\text{Domain:}& x\ge 0\\ \text{Range:}& y\ge 3\end{array}$$ Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or $x\text{-}$value, there is exactly one output, or $y\text{-}$value. From the graph we can see that for each $x\text{-}$value there is exactly one corresponding $y\text{-}$value. Therefore, this relationship is a function.