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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.

Graphs of Function Name if even odd or neither x4 x see attached graph and I only want help with number 1 I want to learn so I can do the rest on my own class=

Respuesta :

semsee45

Answer:

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) [tex]\sf y=6x^5[/tex] is an odd function, as it has symmetry about the origin.

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

Therefore, [tex]\sf y=6x^5-x^3[/tex] is an odd polynomial

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

Ver imagen semsee45
Ver imagen semsee45

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

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