Question

is this function linear, quadratic, or exponential?

x	y
2	4
3	9
4	16
5	25

options: linear, quadratic, exponential

Explanation:

Step1: Check linearity (constant 1st diff)

Calculate first differences of $y$:
$4-1=3$, $9-4=5$, $16-9=7$, $25-16=9$
Differences: $3,5,7,9$ (not constant)

Step2: Check quadratic (constant 2nd diff)

Calculate second differences:
$5-3=2$, $7-5=2$, $9-7=2$
Differences: $2,2,2$ (constant)

Step3: Verify quadratic relationship

Notice $y = x^2$:
$1^2=1$, $2^2=4$, $3^2=9$, $4^2=16$, $5^2=25$ (matches table)

Answer:

quadratic