Even, Odd, or Neither Worksheet
College/Alg Trig 2.2 Even and Odd Functions Name: _______________________We can classify the graphs of functions as either even, odd, or neither.EvenOddA function is an even function if _____________for all x in the domain of f.*The right side of the equation of an even function does NOT change if x is replaced with –x. Even functions are symmetric with respect to the ____________________. This means we could fold the graph on the axis, and it would line up perfectly on both sides!A function is an odd function if ______________for all x in the domain of f.*Every term on the right side of the equation changes signs if x is replaced with –x.Odd functions are symmetric with respect to the ____________________. This means we can flip the image upside down and it will appear exactly the same!If we cannot classify a function as even or odd, then we call it neither!Directions: Determine graphically using possible symmetry, whether the following functions are even, odd, or neither. 1. 2. 3. 4. 5. 6. To verify algebraically if a function is even, odd, or neither, we must prove one of the following.For even prove: _____________________ For odd prove: ____________________If neither of the above are true, we call the function neither!Function NotationWhat to doExample.f(x)Repeat the original function. fx=x2+3x+5f(-x)Plug in a ________ for every x and simplify!fx=x2+3x+5-f(x)Change every sign you see in f(x). If something starts positive, it changes to negative and if it starts negative, it changes to a positive. fx=x2+3x+5Directions: Verify algebraically whether each function is even, odd, or neither!1. fx=x3-6x 2. gx=x4-2x23. hx=x2+2x+14. fx=x2+6 5. gx=7x3-x 6. hx=x5+17. fx=x4-x28. gx=x41+x9. hx=x-110. gx=14x6-5x2 ................
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