Question

Describe how the graph of y=2⋅3x−1 compares to its parent function.(1 point) Responses It is the graph of y=3x with a vertical compression by a factor of 12 and shifted down 1 unit. It is the graph of y equals 3 superscript x baseline with a vertical compression by a factor of Start Fraction 1 over 2 End Fraction and shifted down 1 unit. It is the graph of y=3x with a vertical stretch by a factor of 2 and shifted down 1 unit. It is the graph of y equals 3 superscript x baseline with a vertical stretch by a factor of 2 and shifted down 1 unit. It is the graph of y=3x with a horizontal stretch by a factor of 2 and shifted down 1 unit. It is the graph of y equals 3 superscript x baseline with a horizontal stretch by a factor of 2 and shifted down 1 unit. It is the graph of y=3x with a vertical stretch by a factor of 2 and shifted right 1 unit.

Answer 1

To analyze the graph of the function \( y = 2 \cdot 3^{x-1} \) in comparison to its parent function \( y = 3^x \), we can break down the transformation that has taken place:

1. **Vertical Stretch**: The coefficient of 2 indicates a vertical stretch by a factor of 2. This means that for any value of \( x \), the output of the function \( y = 3^x \) will be multiplied by 2.

2. **Horizontal Shift**: The term \( x - 1 \) shows that the function is shifted to the right by 1 unit. In other words, the entire graph of \( y = 3^x \) will be moved to the right.

Given this analysis, the correct description of how \( y = 2 \cdot 3^{x-1} \) compares to its parent function \( y = 3^x \) is:

**It is the graph of \( y = 3^x \) with a vertical stretch by a factor of 2 and shifted right 1 unit.**