Question

Is the relation depicted in the table below a function? If it is a function, is it linear or nonlinear?
x f(x)
- 2 12
0 2
3 2
5 12
It is a function, linear
It is not a function.
It is a function, nonlinear
It is not a function, but linear.

Answer 1

It is a function, nonlinear.

Reason: Each x-value appears only once, so it’s a function. The slopes between points differ (e.g. slope from x = -2 to 0 is (2−12)/(0−(−2)) = −5, but slope from 0 to 3 is 0), so the points do not lie on a single line.