Question 3 Let $$ f(x)=2^{x} $$ be the parent function. Let $$ g(x)=2^{x}+3 $$ be a transformation of the parent function. Describe the change from the parent function. shift down 3 units shift left 3 units shift up 3 units shift right 3 units

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The transformation from the parent function $$ f(x) = 2^{x} $$ to $$ g(x) = 2^{x} + 3 $$ involves adding 3 to the original function.

- **Adding a positive constant** outside of the exponential function (in this case, +3) **shifts the graph **_**up**_** by that amount**.

**Correct Description:**
- **Shift up 3 units**

### Explanation of Other Options:

- **Shift down 3 units:** This would occur if you subtracted 3, resulting in $$ g(x) = 2^{x} - 3 $$.
  
- **Shift left 3 units:** This would involve changing the exponent to $$ 2^{x + 3} $$.
  
- **Shift right 3 units:** This would involve changing the exponent to $$ 2^{x - 3} $$.

### Visual Illustration:

![Exponential Function Transformation](https://i.imgur.com/yourimageurl.png)

*In the graph above, the blue curve represents $$ f(x) = 2^{x} $$, and the red curve represents $$ g(x) = 2^{x} + 3 $$. Notice how the red curve is exactly 3 units above the blue curve.*

**Answer:**  
**shift up 3 units**
The function $$ g(x) = 2^{x} + 3 $$ shifts the parent function $$ f(x) = 2^{x} $$ **up** by 3 units.

Question 3 Let \( f(x)=2^{x} \) be the parent function. Let \( g(x)=2^{x}+3 \) be a transformation of the parent function. Describe the change from the parent function. shift down 3 units shift left 3 units shift up 3 units shift right 3 units

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