Functions: Even/Odd/Neither. Math I: Unit 5 (Part 2). Graphically…. A function is even…. If the graph is symmetrical about the y-axis, then it’s even. **Fold hotdog!. Graphically…. A function is odd…. If the graph is symmetrical about the y-axis &
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Math I: Unit 5 (Part 2)
If the graph is symmetrical about the y-axis,
then it’s even. **Fold hotdog!
If the graph is symmetrical about the y-axis &
x-axis (or symmetrical about the origin),
then it’s odd. **Fold hotdog & hamburger!
Example 1: f(x) = 2x2 + 5
If you substitute in -x and get the SAME function that you started with, then it’s even.
The equations are exactly the SAME…so EVEN function.
If you substitute in -x and get the OPPOSITE function
(all the signs change),then it’s odd.
Example: f(x) = 4x3 + 2x
EVERY sign changed…so OPPOSITES…
If a function does not have y-axis symmetry OR origin symmetry…then it has NEITHER.
If, after substituting –x in place of x, the equation is not EXACTLY the same OR complete OPPOSITES, then the function is NEITHER.
f(x) = x4 + x2
f(x) = 1 + x3
f(x) = 2x3 + x
SAME – so EVEN
Not same and Not all signs changed – so NEITHER
OPPOSITES– so ODD