7G - Higher order polynomials
■ A function, \(f\), is odd if \(f(-x)=-f(x)\) for all values of \(x\). Geometrically, an odd function remains unchanged after a rotation of \(180^o\) about the origin.
■ A function, \(f\), is even if \(f(-x)=f(x)\) for all values of \(x\). Geometrically, an even function is symmetric about the \(y\)-axis.
■ A function, \(f\), is even if \(f(-x)=f(x)\) for all values of \(x\). Geometrically, an even function is symmetric about the \(y\)-axis.
Odd degree polynomials:
The polynomials \(y=x\) and \(y=x^3\) are examples of odd degree polynomials. Others include:
The polynomials \(y=x\) and \(y=x^3\) are examples of odd degree polynomials. Others include:
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Even degree polynomials:
The polynomials \(y=x^2\) and \(y=x^4\) are examples of even degree polynomials. Others include:
The polynomials \(y=x^2\) and \(y=x^4\) are examples of even degree polynomials. Others include:
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7G - Example 1: Odd and even polynomial functions
7G - Example 2: Odd and even polynomial functions
For each of the following polynomials, determine if the function is odd, even or neither.
(a) \(f(x)=6x^5\) (b) \(f(x)=(x^3-x)^2\) |
7G - Example 2: Video solution
7G - Example 2: Practice
Question 1: ABC Question 2: ABC 7G - Example 2: Solutions
Question 1: ABC Question 2: ABC |