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Describing Domain and Range

Describing Domain and Range 1.14 - Solution

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a

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

By looking at the highlighted points on the graph we can write the minimum and maximum values for and Using the above, we can write the domain and range of the relationship. Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or value, there is exactly one output, or value. Consider the points we have highlighted earlier. We can see that for the input there are two outputs, and Therefore, this relationship is not a function.

b
To determine the domain and range, let's take a look at the given graph.

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

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

By looking at the highlighted points on the graph we can write the minimum and maximum values for and Therefore, we can write the domain and range of the relationship. Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or value, there is exactly one output, or value. From the graph we can see that for each value there is exactly one corresponding 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 is The arrows indicate that the graph continues downwards. This means that all values less than or equal to are possible outputs. Since there are no restrictions, all values are possible inputs. Let's write the domain and range of the relationship. Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or value, there is exactly one output, or value. From the graph we can see that for each value there is exactly one corresponding 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 and values the graph covers. We will recreate the graph, placing points on the minimum and maximum points for and

By looking at the highlighted points on the graph we can write the minimum and maximum values for and Therefore, we can write the domain and range of the relationship. Next, we have to determine whether the relationship is a function. A relationship is a function if for each input, or value, there is exactly one output, or value. Consider the points we have highlighted earlier. We can see that for the input there are two outputs, and 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 and Note that in this case we only need to highlight one point.

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