Answer:
The function f is a linear function.
Step-by-step explanation:
The slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the given table it is noticed that the value of f(x) increased by 7 as the value of x increased by 2.
The first two points are (-5,2.5) and (-3, 9.5).
[tex]m_1=\frac{9.5-2.5}{-3-(-5)}=\frac{7}{2}[/tex]
The last two points are (1,23.5) and (3,30.5).
[tex]m_2=\frac{30.5-23.5}{3-1}=\frac{7}{2}[/tex]
Similarly slope of any two points from the table is [tex]\frac{7}{2}[/tex].
Since the rate of change is constant, therefore the given function is linear.
