f(-x) flips over Y-axis.
-f(x) flips over X-axis.
-f(-x) flips over both X-axis and Y-axis; equivalent to 180° rotation about origin.

If f(x)=f(-x), then f is Even (symmetric across the Y-axis). Also: -f(x)=-f(-x)
If f(-x)=-f(x), then f is Odd (symmetric about the Origin). Also: f(x)=-f(-x)

f(x)= -3x² + 5

f(-x) =
-f(x) =
-f(-x) =
f(3x) =
f(-3x) =
f(x+1) =

f(x)= -3x

f(-x) =
-f(x) =
-f(-x) =
f(3x) =
f(-3x) =
f(x+1) =

f(x)= -3x + 5

f(-x) =
-f(x) =
-f(-x) =
f(3x) =
f(-3x) =
f(x+1) =

f(x)= x³ + 2x² - 3x + 5

f(-x) =
-f(x) =
-f(-x) =
f(3x) =