College/Alg Trig 2.2 Even and Odd Functions Name: _______________________ We can classify the graphs of functions as either even, odd, or neither. Even Odd A function is an even function if _____________ A function is an odd function if ______________ for all x in the domain of f. for all x in the domain of f. *The right side of the equation of an even function *Every term on the right side of the equation does NOT change if x is replaced with changes signs if x is replaced with –x. –x. Even functions are symmetric with respect to Odd functions are symmetric with respect to the ____________________. This means we could the ____________________. This means we can fold the graph on the axis, and it would line up flip the image upside down and it will appear perfectly on both sides! 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.
College/Alg Trig 2.2 Even and Odd Functions Name: _______________________ We can classify the graphs of functions as either even, odd, or neither. Even Odd A 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.
2.2%20Even%20Odd%20Functions.docx