Question

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

$x$	$-3$	$-2$	$-1$	$0$	$1$
$f(x)$	$-567$	$-756$	$-1008$	$-1344$	$-1792$

answer attempt 1 out of 2
this function is because

Explanation:

Step1: Check ratio of consecutive $f(x)$

$\frac{f(-2)}{f(-3)} = \frac{-756}{-567} = \frac{4}{3}$, $\frac{f(-1)}{f(-2)} = \frac{-1008}{-756} = \frac{4}{3}$, $\frac{f(0)}{f(-1)} = \frac{-1344}{-1008} = \frac{4}{3}$, $\frac{f(1)}{f(0)} = \frac{-1792}{-1344} = \frac{4}{3}$

Step2: Identify function type

When consecutive $f(x)$ values have a constant ratio as $x$ increases by 1, the function is exponential.

Answer:

This function is exponential because the ratio of consecutive $f(x)$ values is a constant $\frac{4}{3}$ as $x$ increases by 1.