Question

Compare the functions f(x)=8x
and g(x)=log8x
. The graph of f(x)
contains the points (1,8)
and (−1,0.125)
. Select the answer choice that contains two points on the graph of g(x)
.(1 point)
Responses

(−1,−8)
and (1,−0.125)
left parenthesis negative 1 comma negative 8 right parenthesis and left parenthesis 1 comma negative 0.125 right parenthesis

(1,8)
and (−1,0.125)
left parenthesis 1 comma 8 right parenthesis and left parenthesis negative 1 comma 0.125 right parenthesis

(8,1)
and (0.125,−1)
left parenthesis 8 comma 1 right parenthesis and left parenthesis 0.125 comma negative 1 right parenthesis

(1,0.125)
and (−1,8)

Answer 1

To compare the functions \( f(x) = 8x \) and \( g(x) = \log_8(x) \), we need to find the points on the graph of \( g(x) \) corresponding to the points given for \( f(x) \).

We already know the two points on the graph of \( f(x) \):
1. \( (1, 8) \)
2. \( (-1, 0.125) \)

Now, let's compute \( g(x) \) for \( x = 8 \) and \( x = 0.125 \):

1. For \( f(1) = 8 \):
We want to find \( g(8) \):
\[
g(8) = \log_8(8) = 1
\]
Therefore, the point \( (8, 1) \) is on the graph of \( g(x) \).

2. For \( f(-1) = 0.125 \):
We want to find \( g(0.125) \):
\[
g(0.125) = \log_8(0.125) = \log_8(8^{-1}) = -1
\]
Therefore, the point \( (0.125, -1) \) is on the graph of \( g(x) \).

Thus, the points on the graph of \( g(x) \) are:
- \( (8, 1) \)
- \( (0.125, -1) \)

Now, looking at your options, the correct choice is:
**(8, 1) and (0.125, -1)**.