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:
[tex]\frac{f(0)}{f(-3)}=\frac{8}{8/27}=27[/tex]
Let's now take x=1 and x=-2:
[tex]\frac{f(1)}{f(-2)}=\frac{2/4}{8/9}=\frac{2}{4}\cdot \frac{9}{8}=\frac{18}{32}=\frac{9}{16}[/tex]
And so on:
[tex]\frac{f(2)}{f(-1)}=\frac{7/2}{8/3}=\frac{7}{2}\cdot \frac{3}{8}=\frac{21}{16}[/tex]
[tex]\frac{f(3)}{f(0)}=\frac{2/16}{8}=\frac{2}{16}\cdot 8=\frac{2}{2}=1[/tex]
So, the ratios are:
27 9/16 21/16 1
