Question

Graphs of Function

Name if even, odd or neither
x4 + x²
see attached graph and I only want help with number 1. I want to learn so I can do the rest on my own.

Answer 1

Note:-

Every power of function variables are responsible for even odd like powe is odd function is odd power is even function is even

#1

• x⁴+x²

4 and 2 are even

• Symmetry about y axis

Even

#2

• 6x⁵-x³

5 and 3 are odd

• Symmetry about origin

Odd function

Answer 2

Examine each term of the polynomial to determine whether it is even, odd, or neither.

• Even = each term is an even function
• Odd = each term is an odd function
• Neither = terms are even and odd terms

Even function → symmetry about the y-axis

Odd function → symmetry about the origin

1) y = x⁴ is an even function, as it has symmetry about the y-axis

y = x² is an even function, as it has symmetry about the y-axis

Therefore, x⁴ + x² is an even polynomial

2)
`\sf y=6x^5` is an odd function, as it has symmetry about the origin.

`\sf y=-x^3` is an odd function, as it has symmetry about the origin.

Therefore,
`\sf y=6x^5-x^3` is an odd polynomial

**Please see attachments for examples of even and odd functions**