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 \( (1, 0) \).
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 \( (1, 0) \).