Answer:
The correct choices are shown in bold underline
- y = x³ + 5x:
The function is odd because the table shows symmetry about origin
- y = x + 4
The function is neither because the table does not show symmetry about either the origin or the y-axis
Explanation:
First one has to understand what odd and even functions are
An odd function is symmetric about the origin.
That means f(-x) = -f(x)
An even function is symmetric about the y-axis
That means f(-x) = f(x) ==> you get the same y value for both positive and negative of the same x value
Look at the first function y = x³ + 5 and its associated table
f(1) = 6 and f(-1) = -6
(f(2) = 18 and f(-2) = -18
This satisfies the requirement of an odd function which shows symmetry about the origin
Let's take the second function y = x + 4 and its associated table
We can see that
f(2) = 6 and f(-2) = 2
So it is neither odd nor even