Question

If f(x) =5^x
is the parent function, and f(x) = 1/3 * 5^-x+4 -9

, describe the transformations that took place. Select all that apply.

A
vertical shift 9 units up

B
reflected across the y-axis

C
reflected across the x-axis

D
vertical shift 9 units down

E
vertical stretch by a factor of 3

F
horizontal shrink by a factor of 13\frac{1}{3}
3
1
​


G
vertical shrink by a factor of 13\frac{1}{3}
3
1
​


H
horizontal stretch by a factor of 333

I
horizontal shift 4 units right

J
horizontal shift 4 units left

Answer 1

To analyze the function \( f(x) = \frac{1}{3} \cdot 5^{-x} + 4 - 9 \), we can break it down step by step and compare it to the parent function \( f(x) = 5^x \).

1. **Reflected across the y-axis**: The term \( 5^{-x} \) indicates a reflection across the y-axis, as it represents \( f(-x) \).

2. **Vertical shrink by a factor of 3**: The coefficient \( \frac{1}{3} \) in front of \( 5^{-x} \) indicates a vertical shrink by a factor of 3.

3. **Vertical shift**: The constant \( +4 - 9 \) simplifies to \( -5 \). Therefore, there is a vertical shift of 5 units down.

Putting this together, we can summarize the transformations:

- B: Reflected across the y-axis
- G: Vertical shrink by a factor of 3
- D: Vertical shift 5 units down (Note: the original option stated "9 units down," but it should be "5 units down" based on the calculation).

Therefore, the correct choices are:
- **B** (reflected across the y-axis)
- **G** (vertical shrink by a factor of 3)
- **D** (vertical shift 5 units down)

Since none of the options correctly state "vertical shift 5 units down," you may want to add a note about the actual transformation based on calculation.