Identify the following exponential function as being growth or decay.

﻿f left parenthesis x right parenthesis equals negative 3 to the power of x minus 2﻿

The given exponential function is:

\[
f(x) = -3^{x-2}
\]

Let's break this down:

1. **Exponential Growth/Decay**: Exponential functions take the general form \( f(x) = a \cdot b^x \), where:
   - \( a \) is the initial value (constant multiplier),
   - \( b \) is the base of the exponential term.

   If \( b > 1 \), the function represents exponential **growth**. If \( 0 < b < 1 \), it represents exponential **decay**.

2. **Analyzing \( -3^{x-2} \)**:
   - The base of the exponent is \( 3 \), which is greater than 1. This suggests exponential **growth**.
   - However, the function also has a **negative sign** in front, meaning it will reflect over the x-axis.

Despite the reflection caused by the negative sign, the function still represents exponential **growth**, but in the negative direction. It will decrease as \( x \) increases, due to the negative sign, but the magnitude of the function grows exponentially.

### Conclusion:
The function \( f(x) = -3^{x-2} \) represents **exponential growth** with a negative reflection.

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Would you like more details on how the reflection affects the graph? Here are some related questions:

1. How does the reflection impact the behavior of the exponential graph?
2. What happens to the function as \( x \to \infty \)?
3. Can you plot the graph of this function and explain key points?
4. How does the horizontal shift of \( x - 2 \) affect the graph?
5. What would happen if the negative sign in front of the function were removed?

**Tip**: Reflections in functions occur when a negative sign is placed in front of the entire function or the variable. Always check how they impact the shape and behavior of graphs.

Identify the following exponential function as being growth or decay: f(x) = -3^(x-2)

Understand whether the function f(x) = -3^(x-2) represents exponential growth or decay. Learn about exponential functions, reflections over the x-axis, and how the base of the exponent affects growth or decay. Suitable for students in Grades 9-12.

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