How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other? g(x) is the reflection of f(x) over the x-axis. g(x) is the reflection of f(x) over the y-axis. g(x) is the reflection of f(x) over both axes. g(x) and f(x) will appear to be the same function.

The two functions \( f(x) = 0.7(6^x) \) and \( g(x) = 0.7(6^{-x}) \) are related by a reflection over the **y-axis**.

### Explanation:
- \( f(x) = 0.7(6^x) \): This is an exponential function where \( x \) is in the exponent.
- \( g(x) = 0.7(6^{-x}) \): This is also an exponential function, but here, \( x \) is negated in the exponent.

When the exponent of a function is negated (i.e., \( 6^{-x} \) instead of \( 6^x \)), it reflects the graph over the **y-axis**. So, \( g(x) \) is a reflection of \( f(x) \) over the y-axis.

Thus, the correct answer is:
**g(x) is the reflection of f(x) over the y-axis.**

Would you like more details or have any other questions?

### Related questions:
1. What is the general formula for reflecting a function over the x-axis and y-axis?
2. How would the functions change if the base was less than 1 instead of 6?
3. How does the graph of an exponential function behave as x approaches infinity or negative infinity?
4. Can you derive an equation that reflects \( f(x) \) over both axes?
5. How would adding a constant outside the exponential term affect the function's graph?

**Tip:** Negating the exponent in an exponential function reflects it over the y-axis, while negating the whole function reflects it over the x-axis.

Explore the relationship between exponential functions f(x) = 0.7(6^x) and g(x) = 0.7(6^-x), focusing on how g(x) reflects f(x) over the y-axis. This problem covers key concepts like graph reflections and exponential behavior, suitable for Grades 9-11.

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