Question

is this function linear, quadratic, or exponential?

x | y
-1 | 1.2
0 | 3.6
1 | 10.8
2 | 32.4
3 | 97.2

linear quadratic exponential

Explanation:

Step1: Check linear (constant first differences)

Calculate differences between consecutive $y$-values:
$3.6 - 1.2 = 2.4$
$10.8 - 3.6 = 7.2$
$32.4 - 10.8 = 21.6$
$97.2 - 32.4 = 64.8$
Differences are not constant, so not linear.

Step2: Check quadratic (constant second differences)

Calculate differences of the first differences:
$7.2 - 2.4 = 4.8$
$21.6 - 7.2 = 14.4$
$64.8 - 21.6 = 43.2$
Second differences are not constant, so not quadratic.

Step3: Check exponential (constant ratio)

Calculate ratios of consecutive $y$-values:
$\frac{3.6}{1.2} = 3$
$\frac{10.8}{3.6} = 3$
$\frac{32.4}{10.8} = 3$
$\frac{97.2}{32.4} = 3$
Ratios are constant, so it is exponential.

Answer:

exponential