Question

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

What is the ratio of outputs for any two inputs that are one value apart?



−2
−12
4
2

x −3 −2 −1 0 1 2 3
f(x) −18 −14 −12 −1 −2 −4 −8

Answer 1

The answer should be 4 −8

Answer 2

`r=2`

Explanation:

1) Rewriting the table below:

(Check the graph below)

2) Inputs( x-values) and the outputs are dependent variables (y).

Picking two points

`(-3,(-1)/(8)), (-2,(-1)/(4) )`

3) Similarly to a Geometric Sequence. Looking to the f(x) row to find the ratio, we need always to divide the later term over the previous one:

`r=(y_(2))/(y_(1))=(y_(3))/(y_(2))=(...)=(y_(n+1))/(y_(n))`

4) Hence,

`r=((-1)/(4))/((-1)/(8))\Rightarrow r=(-1)/(4)*-8 \Rightarrow r=(-8)/(-4)=2`