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) .

Answers

GPT-4o mini
To analyze the functions \( f(x) = 8x \) and \( g(x) = \log_8(x) \), we can evaluate \( g(x) \) at specific values to find points that lie on its graph.

The function \( f(x) \) is an exponential function that returns \( 8 \) raised to the value of \( x \):

- \( f(1) = 8^1 = 8 \) (point: \( (1, 8) \))
- \( f(-1) = 8^{-1} = \frac{1}{8} = 0.125 \) (point: \( (-1, 0.125) \))

Next, we will find appropriate points for \( g(x) = \log_8(x) \). This function gives us the exponent to which the base \( 8 \) must be raised to yield \( x \).

### Evaluating \( g(x) \):
1. **For \( x = 8 \)**:
\[
g(8) = \log_8(8) = 1 \quad \text{(point: (8, 1))}
\]

2. **For \( x = 1 \)**:
\[
g(1) = \log_8(1) = 0 \quad \text{(point: (1, 0))}
\]

3. **For \( x = \frac{1}{8} \)**:
\[
g\left(\frac{1}{8}\right) = \log_8\left(\frac{1}{8}\right) = -1 \quad \text{(point: \(\left(\frac{1}{8}, -1\right)\))}
\]

Thus, we have identified the following two points on the graph of \( g(x) \):
- \( (8, 1) \)
- \( (1, 0) \)

If you are looking for two points on the graph of \( g(x) \), you could use \( (8, 1) \) and \( (1, 0) \).

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