Question

The equations of two exponential functions are shown.

F(x)=9(3/8)^x
G(x)=9(8/3)^x

Which 2 statements about the graphs of functions are true
(Pick 2)

They have the same slope

They have the same x intercept

They have the same y intercept

They are both increasing functions

They are both decreasing functions

Answer 1

To analyze the two functions \( F(x) = 9(3/8)^x \) and \( G(x) = 9(8/3)^x \), we can look at their general properties:

1. **Y-Intercept**: Both functions have the same y-intercept because when \( x = 0 \):
- \( F(0) = 9(3/8)^0 = 9 \)
- \( G(0) = 9(8/3)^0 = 9 \)
Thus, both functions have the same y-intercept at \( (0, 9) \).

2. **X-Intercept**: To find \( x \)-intercepts, we set \( F(x) \) and \( G(x) \) equal to zero. However, both exponential functions do not cross the x-axis, as they never equal zero for any real \( x \). Therefore, they do not have an x-intercept.

3. **Increasing or Decreasing Functions**: The base of the exponential function for \( F(x) \) is \( \frac{3}{8} \), which is less than 1, indicating that \( F(x) \) is a decreasing function. Conversely, the base of \( G(x) \) is \( \frac{8}{3} \), which is greater than 1, indicating that \( G(x) \) is an increasing function.

4. **Slope**: Exponential functions do not have a constant slope; their rates of growth change. Therefore, they do not have the same slope.

Based on this analysis, the two true statements about the graphs of the functions are:

- **They have the same y intercept.**
- **They are both decreasing functions.**

Hence, the correct answers are:
- They have the same y intercept.
- They are both decreasing functions.