I need help or I could fail this class

Question

Use the graph to answer the question. 

© 2018 StrongMind. Created using GeoGebra.

 Is the function even, odd, or neither? Why?

A. The function is odd because it is symmetric about the origin.

B. The function is odd because it is symmetric about the y-axis.

C. The function is neither even nor odd because it is not symmetric about the y-axis or the origin.

D. The function is even because it is symmetric about the y-axis.

E. The function is even because it is symmetric about the origin.

Answer 1

A. The function is odd because it is symmetric about the origin.

You can see the symmetry by choosing a point, for example (-1,5), and then checking to see if the opposite

y-value (-5) occurs on the graph when you choose the inverse (1) of the x-value. Since the point (1,-5) occurs on the graph, the function is odd.

Answer 2

Alyssa R. is correct. For a function to be odd, when a number's opposite -x is used as input, the output value is also the opposite (or multiplied by -1).

In function notation, an odd function is written -f(x)=f(-x), where f(-x) is the opposite of the input value, and -f(x) is the opposite of the output value.

Use (1, -5) which is on the graph. When the opposite input (-1) is used, the opposite output (5) is also on the graph. The function is odd.