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

Answer:

B.

Step-by-step 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 $y=-\frac{1}{8}$

$y=8(4)^{x-1} \\y=8(4)^{-2-1}\\ y=8(4)^{-3}\\ y=\frac{8}{4^{3} }=\frac{1}{8}$

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

$y=-8(4)^{x-1}\\ y=-8(4)^{-2-1}\\ y=-8(4)^{-3}\\ y=-\frac{8}{4^{3} }=-\frac{1}{8}$

Let's evalute for $x=0$

$y=-8(4)^{0-1}=-8(4)^{-1}= -\frac{8}{4}=-2$

Which is right.

Therefore, the right answer is B.