Question

What’s the difference between y=f(-x) and y=-f(x) ?

Answer 1

The difference between y=f(-x) and y=-f(x) is that the former reflects a horizontal reflection of the function f(x) across the y-axis, while the latter reflects a vertical reflection of the function f(x) across the x-axis. In other words, when you replace x with -x in the function f(x), you are reflecting the graph of the function across the y-axis. On the other hand, when you negate the entire function f(x), you are reflecting the graph across the x-axis.

Answer 2

The function y = f(-x) is the reflection of the function f(x) about the y-axis. In other words, it is obtained by replacing x with -x in the function f(x).

On the other hand, the function y = -f(x) is obtained by reversing the sign of the output values of the function f(x). This means that for any given value of x, the corresponding value of y for the function y = -f(x) will have the opposite sign of the corresponding value of y for the function f(x).

In other words, y = -f(x) will reflect the function f(x) about the x-axis.