If g(x) is an odd function, which function must be an even function?
f(x) = g(x) + 2
f(x) = g(x) + g(x)
f(x) = g(x)2
f(x) = –g(x)

C.  f(x) = g(x)²

Step-by-step explanation:

An even function is a function that gives symmetric result when you reflect it on the y-axis. That means the result of f(-x) will be equal to f(x). An odd function will give similar results but mirrored to x-axis too, so f(-x) will equal to -f(x).  

Odd or even function depends on the highest degree of x of the function. If the degree is even (like x²) it will be even function, but if its odd(like x³) it will be odd.  

Translating, dilating, or mirroring the function will not change it from even to odd. To change odd function into even function, you have to change the degree too:

f(x) = g(x) + 2  this function translate  

f(x) = g(x) + g(x)  this function dilate

f(x) = –g(x) this function mirror

The answer will be f(x) = g(x)² since this function changes the degree and multiply it by two. Any odd degree will become even if its multiplied by even number.

the graph on the bottom right

b. 2 and 4

step-by-step explanation: