Question

This table shows the input and output values for an exponential function f(x) .

Answer 1

Answer:

27  9/16  21/16  1

Step-by-step explanation:

The table with the input and output values for the exponential function is the following:

x −3 −2 −1 0 1 2 3

f(x) 8/27 8/9 8/3 8 2/4 7/2 2/16

Now we have to take three output values that are three values apart and calculate their ratio. Let's take x=0 and x=-3. The output ratio is:

$\frac{f(0)}{f(-3)}=\frac{8}{8/27}=27$

Let's now take x=1 and x=-2:

$\frac{f(1)}{f(-2)}=\frac{2/4}{8/9}=\frac{2}{4}\cdot \frac{9}{8}=\frac{18}{32}=\frac{9}{16}$

And so on:

$\frac{f(2)}{f(-1)}=\frac{7/2}{8/3}=\frac{7}{2}\cdot \frac{3}{8}=\frac{21}{16}$

$\frac{f(3)}{f(0)}=\frac{2/16}{8}=\frac{2}{16}\cdot 8=\frac{2}{2}=1$

So, the ratios are:

27  9/16  21/16  1