Consider the following graph:
What is the slope/rate of change between the inputs of 0 and 3?
What is the slope/rate of change between the domain values of 3 and 6?
Is the slope/rate of change constant (not changing/the same)?
Is the function linear?
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Is the function linear?
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To determine the slope/rate of change between the inputs of 0 and 3, we can calculate the change in the outputs. From the graph, we can see that the output at x = 0 is -2 and the output at x = 3 is 4.
Therefore, the change in output is 4 - (-2) = 6.
The change in the input is 3 - 0 = 3.
So, the slope/rate of change between the inputs of 0 and 3 is 6/3 = 2.
Similarly, to determine the slope/rate of change between the domain values of 3 and 6, we can calculate the change in the outputs. From the graph, we can see that the output at x = 3 is 4 and the output at x = 6 is 6.
Therefore, the change in output is 6 - 4 = 2.
The change in the input is 6 - 3 = 3.
So, the slope/rate of change between the domain values of 3 and 6 is 2/3.
Since the slope/rate of change is different between the two intervals, the slope/rate of change is not constant.
Based on the given information and the graph, it is difficult to determine if the function is linear without more information.