Respuesta :

Answer:

D. The function is odd because it is symmetric with respect to the origin.

Step-by-step explanation:

We have been given a graph of a function. We are asked to determine whether our given function is odd or even.

We know that a function is even, when it is symmetric with respect to the y-axis.

We also know that a function is odd, when it is symmetric with respect to the origin.

Upon looking at our given graph, we can see that it is symmetric about the origin, therefore, option D is the correct choice.

BladeRunner212

The function is odd because it is symmetric with respect to the origin.

(Option D)

Further explanation

We will determine whether the function is shown in the graph is even or odd.

Let us recall how to distinguish whether the function graph is included in an even or odd function.

Even Functions

  • A function f is even if, for each x in its domain, [tex]\boxed{ \ f(-x) = f(x) \ }[/tex].
  • The graph of an even function is symmetric with respect to the y-axis.
  • In order to complete the graph for an even function just imagine the y-axis as a mirror and draw the reflection of each point on the other side.
  • Examples: [tex]\boxed{ \ f(x) = x^2 \ } \boxed{ \  f(x) = 2x^4 - 4 \ } \boxed{ \ f(x) = sin \ x \ for \ -360^0 \leq x \leq 360^0 \ }[/tex]

Odd Functions

  • A function f is odd if, for each x in its domain, [tex]\boxed{ \ f(-x) = -f(x) \ }[/tex].
  • The graph of an odd function is symmetric with respect to the origin.
  • In order to complete the graph for an odd function connect each point with the origin and extend that line to the other side of the origin until we have the same distance.
  • Examples: [tex]\boxed{ \ f(x) = x^3 \ } \boxed{ \  f(x) = 2x^3 - 4x \ } \boxed{ \ f(x) = \frac{x^2 + 1}{2x} \ } \boxed{ \ f(x) = tan \ x \ }[/tex]

Generally, the functions that we face are neither even nor odd.

Learn more

  1. Which table represents a linear function https://brainly.com/question/10570936
  2. The piecewise-defined functions https://brainly.com/question/9590016
  3. The functions that inverse of each other https://brainly.com/question/4620451
Ver imagen BladeRunner212