Question

In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x) = 3^x to obtain the graph of f(x)=3^-x+1 -2.

a) True
b) False

Answer 1

The parent function f(x) = 3^x undergoes a horizontal shift to the right by 1, a reflection across the x-axis, and a vertical shift down by 2 to obtain the graph of f(x) = 3^-x+1 -2.

Step-by-step explanation:

Transformation of the Function f(x) = 3^x to f(x) = 3^-x+1 -2

To obtain the graph of the function f(x) = 3^-x+1 -2 from the parent function f(x) = 3^x, the following transformations occur:

Horizontal Shift to the Right by 1: The entire graph of the function is shifted right by 1 unit.

Reflection across the x-axis: The graph is flipped over the x-axis, resulting in a reflection of the function.

Vertical Shift Down by 2 units: The entire graph of the function is shifted down by 2 units.

These transformations alter the parent function to produce the graph of f(x) = 3^-x+1 -2.