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 1 comma 8 right parenthesis and left parenthesis negative 1 comma 0.125 right parenthesis

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

(−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

(8,1)
and (0.125,−1)

Answer 1

To find points on the graph of \( g(x) = \log_8 x \), we first need to determine the values of \( g(x) \) at specific \( x \) values.

Given:

1. For \( x = 1 \):
\[
g(1) = \log_8(1) = 0 \quad (\text{since } 8^0 = 1)
\]
So, the point is \( (1, 0) \).

2. For \( x = -1 \):
The logarithm function \( g(x) = \log_8 x \) is only defined for positive \( x \). Therefore, \( g(-1) \) is undefined.

Now, let's check if there are any logical points for \( g \) in the answer choices:

- The other potential candidates \( x = 8 \) and \( x = 0.125 \):

For \( x = 8 \):
\[
g(8) = \log_8(8) = 1 \quad (\text{since } 8^1 = 8)
\]
So, the point is \( (8, 1) \).

For \( x = 0.125 \):
\[
g(0.125) = \log_8(0.125) = -1 \quad (\text{since } 8^{-1} = 0.125)
\]
So, the point is \( (0.125, -1) \).

The only answer choice that correctly describes points on the graph of \( g(x) \) is:

\[
(8, 1) \quad \text{and} \quad (0.125, -1)
\]

Thus, the correct answer is:

**(8, 1) and (0.125, -1)**.