the graph shows a function. is the function even, odd, or neither? use the drop - down menus to explain…

the graph shows a function. is the function even, odd, or neither? use the drop - down menus to explain. click the arrows to choose an answer from each menu. for the function on the graph, opposite x - values have choose... y - values. this shows the function is choose... because its graph has choose...

the graph shows a function. is the function even, odd, or neither? use the drop - down menus to explain. click the arrows to choose an answer from each menu. for the function on the graph, opposite x - values have choose... y - values. this shows the function is choose... because its graph has choose...

Answer

Explanation:

Step1: Recall function - type definitions

An even function has (f(x)=f( - x)) (symmetric about y - axis), and an odd function has (f(-x)=-f(x)) (symmetric about the origin).

Step2: Analyze the graph

Looking at the graph, if we take a point ((x,y)) on the graph and its opposite (x) - value ((-x)), the (y) - values are opposite. For example, if ((x,y)) is on the graph, then ((-x, - y)) is on the graph.

Step3: Determine the function type

Since for opposite (x) - values, the (y) - values are opposite, the function satisfies (f(-x)=-f(x)), so it is an odd function. The graph of an odd function is symmetric about the origin.

Answer:

For the function on the graph, opposite (x) - values have opposite (y) - values. This shows the function is odd because its graph has origin symmetry.