Question

determine if the function below is linear or exponential then fill in the guided sentences below.

$x$	1	2	3	4

answer attempt 1 out of 2

the function is \\(\square\\) because as $x$ increases, the $y$ values change \\(\square\\). the \\(\square\\) of this function is exactly \\(\square\\).

Explanation:

Step1: Check linearity (constant difference)

Calculate differences: $9-3=6$, $27-9=18$, $81-27=54$. Differences are not constant.

Step2: Check exponential (constant ratio)

Calculate ratios: $\frac{9}{3}=3$, $\frac{27}{9}=3$, $\frac{81}{27}=3$. Ratios are constant.

Step3: Identify function type and ratio

Function is exponential; constant ratio is 3.

Answer:

The function is exponential because as $x$ increases, the $y$ values change by a constant multiplicative factor. The common ratio of this function is exactly $\boldsymbol{3}$.