Question

What transformation of the parent function (f(x)) is made to get (f(-x) + 1)?

a) A reflection in the x-axis and 1 unit in the y-direction
b) A reflection in the x-axis and -1 unit in the y-direction
c) A reflection in the y-axis and -1 unit in the y-direction
d) A reflection in the y-axis and 1 unit in the y-direction

Answer 1

The transformation of the parent function (f(x)) to get (f(-x) + 1) is a reflection in the y-axis and 1 unit in the y-direction.

Step-by-step explanation:

The transformation of the parent function (f(x)) to get (f(-x) + 1) is a reflection in the y-axis and 1 unit in the y-direction.

To understand this transformation, let's consider the parent function f(x). When we replace x with -x in the function, it reflects the graph of f(x) in the y-axis. This is because replacing x with -x essentially flips the graph horizontally. So, the function becomes f(-x).

Adding 1 to f(-x) results in raising the graph of f(-x) by 1 unit in the y-direction. Therefore, the transformation of the parent function f(x) to get (f(-x) + 1) is a reflection in the y-axis and 1 unit in the y-direction.