Notes

Problems and Videos

\(\textbf{1)}\) Verify the following function is odd. \( f(x)=4x^3-2x \)
See Video for answer.

 

\(\textbf{2)}\) Verify the following function is even. \( f(x)=4x^4-2x^2+5 \)
See Video for answer.

 

For numbers 3-5, are the following functions even, odd or neither?

\(\textbf{3)}\) \( f(x)=2x^2+5 \)

Even, Odd or Neither?

This Function is Even

 

\(\textbf{4)}\) \( f(x)=5x^3+5 \)

Even, Odd or Neither?

This Function is Neither

 

\(\textbf{5)}\) \( f(x)=6x^3+2x \)

Even, Odd or Neither?

This Function is Odd

 

\(\textbf{6)}\) Even, odd or neither?

Show Answer

This Function is Neither

 

\(\textbf{7)}\) Even, odd or neither?

Show Answer

This Function is Odd (Note it is symmetric about the origin)

 

\(\textbf{8)}\) Even, odd or neither?

Show Answer

This Function is Even (Note it is symmetric over y-axis

 

See Related Pages\(\)

\(\bullet\text{ Composite Functions}\)
\(\,\,\,\,\,\,\,\,(f\circ g)(x)=f(g(x))\)

\(\bullet\text{ Inverse Functions and Relations}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\frac{x+3}{2}\)

\(\bullet\text{ Operations of Functions}\)
\(\,\,\,\,\,\,\,\,(f+g)(3)=f(3)+g(3)\)