Question

The function f(x) = x^2 is transformed to create the function g(x) = -1f(x). What statement is true comparing f(x) and g(x).

a) g(x) opens upward, but does not get wider nor narrower
b) g(x) opens downward, but does not get wider nor narrower
c) g(x) opens upward and is wider
d) g(x) opens downward and is wider.

Answer 1

The function g(x) = -1f(x) opens downward, but does not get wider nor narrower.

Step-by-step explanation:

To transform the function f(x) = x^2 to create the function g(x) = -1f(x), we multiply f(x) by -1. This means that the graph of g(x) reflects the graph of f(x) across the x-axis. Since the original function f(x) = x^2 opens upward, the transformed function g(x) will open downward. However, the transformation does not affect the width of the graph, so g(x) does not get wider or narrower than f(x). Therefore, the correct statement is option b) g(x) opens downward, but does not get wider nor narrower.