Think of f(x) as the y value If you add 2 to y you move the function up by 2 units. The shape stays the same, where it is increasing and decreasing stays the same. It's just an upward shift. If f(x) is an even function, this means f(-x) = f(x), so what I just described applies If f(x) is an odd function, this means f(-x) = -f(x), so what I just described applies as as well When you multiply f(x) by -1/2, you invert the function f(x) so that positive values become negative and negative become positive. This means where f(x) was maximum, it's now a minimum and vice-versa If f(x) is even, then what I've just described applies If f(x) is odd, then what I've just described applies Hope this helps.