3.) The function $$ g $$ is related to one of the parent functions $$ g(x)=-(x-2)^{\wedge} 3 $$ a.) Identify the parent function $$ f $$. b.) Use function notation to write $$ g $$ in terms of $$ f $$.

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Let's analyze the function $$ g(x) = -(x - 2)^3 $$ to identify its parent function and express it in terms of that parent function.

### a.) Identify the Parent Function $$ f $$

The **parent function** is the simplest form of a family of functions, without any transformations like shifts, stretches, or reflections. In the given function:

$$ g(x) = -(x - 2)^3 $$

The part $$(x)^3$$ represents the simplest form of a cubic function, which is the parent function.

**Parent Function:**
$$ f(x) = x^3 $$

### b.) Express $$ g $$ in Terms of $$ f $$ Using Function Notation

To express $$ g $$ in terms of the parent function $$ f $$, we need to identify how $$ g $$ is transformed from $$ f $$:

1. **Horizontal Shift:** The term $$(x - 2)$$ indicates a shift to the right by 2 units.
2. **Reflection:** The negative sign in front of the function $$-$$ indicates a reflection over the x-axis.

Using these transformations, we can write $$ g $$ in terms of $$ f $$:

$$ g(x) = -f(x - 2) $$

**Final Expressions:**

a.)  
$$ f(x) = x^3 $$

b.)  
$$ g(x) = -f(x - 2) $$
a.) The parent function is $$ f(x) = x^3 $$. b.) $$ g(x) = -f(x - 2) $$.

3.) The function \( g \) is related to one of the parent functions \( g(x)=-(x-2)^{\wedge} 3 \) a.) Identify the parent function \( f \). b.) Use function notation to write \( g \) in terms of \( f \).

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