1.5B Polynomial functions and complex zeros
Define an even function. How is it graphically represented?
Define an odd function. How is it graphically represented?
What does the property f (−x) = f (x) signify about a function?
Consider the function p(x) = a_n x^n, where n ≥ 1 and an ≠0. If n is even, is the function even or odd?
Determine if the following functions are even, odd or neither based on their symmetry:
f \left( x \right) = x^3 - x
f \left( x \right) = x^4 - 3x^2 + 2
f \left( x \right) = x^5 - 4x^3 + 2x
f \left( x \right) = x^2 + 2x + 1
For each of the given functions, state whether the graph is symmetric about the y-axis, the x-axis, the origin, or is not symmetric:
f \left( x \right) = x^2 - 4x + 4
f \left( x \right) = x^3 + 3x^2 - x - 3
f \left( x \right) = x^3 - 6x
f \left( x \right) = 2x^4 - 8x^2 + 2
Determine whether the following polynomial functions are even, odd, or neither:
Given the graph of a polynomial function below, determine if the function is even, odd, or neither:
Determine whether the following graphs are even, odd, or neither. Justify your answer.
A polynomial function has the following properties:
It is a cubic function.
The function is symmetric about the origin.
Determine if the function is even, odd, or neither.
Given the polynomial function f(x) = 4x^5 - 2x^3 + x, determine whether it is even, odd, or neither. Justify your answer using the properties of even and odd functions.
The function f(x) = x^4 - 2x^2 + 1 is said to be even. Provide a demonstration to justify this statement.
The function f(x) = x^3 - 3x is said to be odd. Provide a demonstration to justify this statement.
Can a function be both even and odd at the same time? Justify your answer.
Consider the function f(x) = 3x^4 - 5x^2 + 2. Is this function even, odd or neither? Justify your answer.