Even and Odd polynomial functions

Need TI 84 calculator (can be found online) For trig functions (cos sin tan) put your calculator in radian mode

What is an even function? (def)

A function that is symmetrical about the y-axis

What is the term for a even function?

f(-x)

For a function to be a even function what has to be true?

f(-x)= f(x)

For a function to be a odd function what has to be true?

f(-x)= -f(x)

What is the term for a odd function?

-f(x)

What is an odd function? (def)

A function the is symmetric with respect to the origin (if you rotate the graph 180 degrees, you will have the same function you started with)

If the bottom two equations on the table are equal the function is…

Odd

If the top two equations on the table are equal the function is…

even

If a negative variable is raised to an odd exponent, the result is always _____

negative

If a negative variable is raised to an even exponent, the result is always _____

positive

(-x)² =?

x²

(-x)⁸ =?

x⁸

Is (-2)³ positive or negative?

Negative

(-x)⁷ =?

-x⁷

(-x)⁶³ =?

-x⁶³

If f(-x) = -f(x) than the function is ___

odd

If f(-x) = f(x) than the function is ___

even

If f(x) = -f(x) than the function is ___

It doesn’t make sense

If no f(x) isn’t equal to anything than…

it is neither

If f(x)= 3ײ + 2x, find f(-x)

f(-x) = 3ײ - 2x

Determine if the following function is even, odd, or neither:

f(x) = x³ - 6x

The function is odd

Determine if the function is even, odd, or neither:

f(x) = x³ - x² + 4x + 2

Neither

Determine whether the function f(x) = 7x + 5×⁵ - 7×⁷ is even, odd, or neither.

f(x) is odd

Determine whether the function f(x) = -1 + 6×⁶ - 9ײ is even, odd, or neither.

f(x) is even

Determine whether the function f(x) = -3׳ + 7×⁵ is even, odd, or neither.

f(x) is odd

Determine whether the function f(x) = 9׳ + 8 is even, odd, or neither.

f(x) is neither

Determine whether the function f(x) = 3 + x⁴ is even, odd, or neither.

f(x) is even

Determine whether the function f(x) = -4×⁵ - 7x - 8×⁷ is even, odd, or neither.

f(x) is odd

Determine whether the function f(x) = -6ײ + x⁴ - 7×⁶ is even, odd, or neither.

f(x) is even

Determine whether the function f(x) = -3x + 1 is even, odd, or neither.

f(x) is neither

Determine whether the function f(x) = -x - x⁷ is even, odd, or neither.

f(x) is odd

Fill out the table and what type of function it is. Hint: plug in the x.

-161, -6, -1, 4, 159

neither

Fill out the table and what type of function it is.

8.74, -6.229, 0, 6.229, -8.74

odd

Fill out the table and what type of function it is.

6,3,0,3,6

even

If the opposite x value on the table (ex: 2 and -2) have the same number but opposites, the function is…

odd

If the opposite x value (ex. 1 and -1) has the same exact number, the function is…

even

Whenever you replace a variable with a number, always remember, no matter what, to…

put it in parenthesis

Fill out the table and what type of function it is.

-168, -6, 0, 6, 168

odd

Fill out the table and what type of function it is.

-6.08, -1.298, 0, -6.08, -1.298

Fill out the table and what type of function it is.

72,4,0,6,88

neither