Question

Compare the functions f(x)=8
x
and g(x)=log
8
​
x. 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).
A. (1,8) and (−1,0.125)
B. (−1,−8) and (1,−0.125)
C. (8,1) and (0.125,−1)
D. (1,0.125) and (−1,

Answer 1

To analyze the functions \( f(x) = 8^x \) and \( g(x) = \log_8 x \), we can compute the values of \( g(x) \) at specific points to find corresponding points on its graph.

1. **Calculate points on \( f(x) \):**
- \( f(1) = 8^1 = 8 \) giving the point \( (1, 8) \).
- \( f(-1) = 8^{-1} = \frac{1}{8} = 0.125 \) giving the point \( (-1, 0.125) \).

2. **Calculate points on \( g(x) \):**
- To find points on \( g(x) = \log_8 x \):
- \( g(8) = \log_8 8 = 1 \) giving the point \( (8, 1) \).
- \( g(0.125) = \log_8 0.125 \). Since \( 0.125 = 8^{-1} \), we find that \( g(0.125) = -1 \), giving the point \( (0.125, -1) \).

Now we compare the computed points on \( g(x) = \log_8 x \):
- We have the points \( (8, 1) \) and \( (0.125, -1) \).

Now we can find the correct answer choice:
- **Choice A**: Contains points from \( f(x) \).
- **Choice B**: Contains invalid points.
- **Choice C**: Contains the points \( (8, 1) \) and \( (0.125, -1) \).
- **Choice D**: Is incomplete.

Thus, the correct answer is **C. (8,1) and (0.125,−1)**.