Question

compare the graphs of y=f(x) and y=-f(x)

Answer 1

the second function has the same values as the first function, except they are negated. see why?

Answer 2

Because the f is negative?

Answer 3

yes. say f(x) is any function in the world. you plug in a value, x, and you get f(x). if you came up with another function called -f(x), it's the same exact thing as the first function except the output is multiplied by -1

Answer 4

What if the x was negative instead of the f, would it be divided? Or multiplied...

Answer 5

like f(x) compared to f(-x) ?

Answer 6

Yes.

Answer 7

f(x) = f(-x) means that the function is symmetrical about the y-axis.

example




f(x) = x^2 , and f(-x) = (-x)^2 = x^2 = f(x). see how this function is symmetrical?

Answer 8

if, instead, you had -f(x), this would reflect the function about the x-axis. so start with f(x) = x^2. -f(x) = -x^2 and looks like this: