Question

algebraically determine whether each of the following functions is even, odd or neither. and graph itA.y = |x|-2

Answer 1

Answer:

The function is even

Explanation:

A function is even if f(-x) = f(x). So, for the function y = |x| - 2, we can write f(x) and f(-x) as:

f(x) = | x | - 2

f(-x) = | - x | - 2 = | x | - 2

Since the absolute value of x and -x are equal, we can say that the function is even.

On the other hand, a function is odd if f(-x) = -f(x). So for the function, f(-x) and -f(x) are equal to:

f(-x) = | - x | - 2 = | x | - 2

-f(x) = - ( | x | - 2) = - | x | + 2

Since f(-x) and - f(x) are not equal, the function is not odd.

Finally, the graph of the function is:

Therefore, the function is even.