WarmUp Symmetric about the y axis FUNCTIONS Symmetric

Warm-Up •

Symmetric about the y axis FUNCTIONS Symmetric about the origin

Even functions have y-axis Symmetry 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 For an even function: for every point (x, y) on the graph, the point (-x, y) is also on the graph.

Odd functions have origin Symmetry 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7 For an odd function: for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

x-axis Symmetry We wouldn’t talk about a function with x-axis symmetry because it wouldn’t BE a function. 8 7 6 5 4 3 2 1 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -2 -3 -4 -5 -6 -7

Even, Odd or Neither? Graphically

Even, Odd or Neither? Graphically

Even, Odd or Neither? Graphically

Even, Odd or Neither? Graphically

If you plug a –x into the function and you get the original function back again, the function is even. • Same! Even Function

If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function is odd. • ALL signs of the terms changed! Odd Function

If you plug a –x into the function and you get the original function back again, the function is even. Is this function even? YES Is this function even? NO

If you plug a –x into the function and you get the negative of the function back (all terms change signs), the function is odd. Is this function odd? NO Is this function odd? YES

Odd, Even, or Neither? • Even Function

Odd, Even, or Neither? • Neither Odd or Even

Odd, Even, or Neither? • Odd Function