Question

answer the questions below to determine what kind of function is depicted in the table below.

$x$	$-1$	$0$	$1$	$2$	$3$
$f(x)$	$-13$	$-52$	$-208$	$-832$	$-3328$

answer attempt 2 out of 2

this function is because

Explanation:

Step1: Check ratio of consecutive f(x)

$\frac{f(0)}{f(-1)} = \frac{-52}{-13} = 4$
$\frac{f(1)}{f(0)} = \frac{-208}{-52} = 4$
$\frac{f(2)}{f(1)} = \frac{-832}{-208} = 4$
$\frac{f(3)}{f(2)} = \frac{-3328}{-832} = 4$

Step2: Identify function type

Since the ratio of consecutive $f(x)$ values is constant (4) for equally spaced $x$-values, this is an exponential function.

Answer:

This function is an exponential function because the ratio of consecutive output values is a constant 4 when the input values increase by 1.