The question is missing the table. So, it is attached below.
Answer:
The function is not linear. The student didn't evaluate the rate of change for the given points on the function.
Step-by-step explanation:
Given:
From the table, the set of points of the function are:
(-1, -5), (0, 0), (2,5), (3, 10), and (4, 15)
A function is said to be linear if the rate of change of the function is always a constant.
Rate of change for any two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, the rate of change for the points (-1, -5) and (0, 0) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-(-5)}{0-(-1)}\\\\m=\frac{5}{1}=5[/tex]
Now, the rate of change for the points (0, 0) and (2, 5) is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-0}{2-0}\\\\m=\frac{5}{2}=2.5[/tex]
Hence, we can observe that, the rate of change is different for the given points. Hence, it is not a linear function.
Therefore, the student didn't evaluate the rate of change for the given points on the function.
