Question

Use the drop down menus to describe the transformations of the parent function f(x)=3x that result in the function g(x) = −2⋅3 x + 4 (3 points) The negative negative sign in front of the function results in a . The multiplier 2, results in a by the factor 2. Lastly, the plus 4 in the exponent shifts the graph 4 units.

Answer 1

To describe the transformations of the parent function \( f(x) = 3^x \) that result in the function \( g(x) = -2 \cdot 3^{x + 4} \), we can break it down as follows:

1. The negative sign in front of the function results in a reflection across the x-axis.

2. The multiplier 2 results in a vertical stretch by a factor of 2.

3. Lastly, the plus 4 in the exponent results in a horizontal shift (to the left) of 4 units.

So, the final descriptions are:

1. The negative sign results in a reflection.
2. The multiplier 2 results in a vertical stretch by the factor of 2.
3. The plus 4 in the exponent shifts the graph 4 units to the left.