If the parent cube root function, $$ f(x) $$, is transformed to $$ 2 f(x+5) $$ what will be the effect on the graph?

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To analyze the transformation of the parent cube root function $$ f(x) = \sqrt[3]{x} $$ to $$ 2 f(x+5) $$, we will break down the transformations step by step.

1. **Understanding the Parent Function**:
   - The parent function is $$ f(x) = \sqrt[3]{x} $$. This function has a characteristic shape that passes through the origin (0,0) and is symmetric about the origin.

2. **Transformation $$ f(x+5) $$**:
   - The expression $$ f(x+5) $$ indicates a horizontal shift of the graph to the left by 5 units. This means that every point on the graph of $$ f(x) $$ will move 5 units to the left. For example, the point (0,0) will move to (-5,0).

3. **Transformation $$ 2 f(x+5) $$**:
   - The multiplication by 2 in $$ 2 f(x+5) $$ indicates a vertical stretch of the graph by a factor of 2. This means that for every y-coordinate of the points on the graph of $$ f(x+5) $$, we will multiply it by 2. For example, if a point on $$ f(x+5) $$ is (-5,0), it will remain at (-5,0) after the stretch, but if there was a point at (-4, y), it will move to (-4, 2y).

### Summary of Effects on the Graph:
- **Horizontal Shift**: The graph shifts 5 units to the left.
- **Vertical Stretch**: The graph is stretched vertically by a factor of 2.

Thus, the overall effect on the graph of the parent cube root function $$ f(x) $$ when transformed to $$ 2 f(x+5) $$ is a leftward shift of 5 units and a vertical stretch by a factor of 2.
The graph shifts 5 units to the left and stretches vertically by a factor of 2.

If the parent cube root function, \( f(x) \), is transformed to \( 2 f(x+5) \) what will be the effect on the graph?

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