Question

The following table represents a function.

x y
-2 -1/8
-1 -1/2
0 -2
1 -8
2 -32

Which exponential function does this table represent?

A. y = 8(4)^(x-1)
B. y = -8(4)^(x-1)
C. y = 8(1/4)^(x-1)
D. y = -8(1/4)^(x-1)

Answer 1

The answer is B. Plug in the x values to check the y values.

Answer 2

B.

Explanation:

To find the right exponential function, we can just take x-values an replace them into the given functions. The one that give the correct y-values will be the answer.

For
`x=-2`, let's see which function gives
`y=-(1)/(8)`

`y=8(4)^(x-1) \\y=8(4)^(-2-1)\\ y=8(4)^(-3)\\ y=(8)/(4^(3) )=(1)/(8)`

You can observe that function A is not the correct one, because it gives a positive result. However, function B can actually be the answer, because it woud give the same y-value than A but negative, as we need. Let's see

`y=-8(4)^(x-1)\\ y=-8(4)^(-2-1)\\ y=-8(4)^(-3)\\ y=-(8)/(4^(3) )=-(1)/(8)`

Let's evalute for
`x=0`

`y=-8(4)^(0-1)=-8(4)^(-1)= -(8)/(4)=-2`

Which is right.

Therefore, the right answer is B.