Answer:
B
Explanation:
I cannot see option D but regardless, C is a function for the following reasons
A function y = f(x) is a relationship in x such that f(x) has only 1 value for a value of x.
In A, we see that for x = -1 we have y = 2 and y = 4 for a single value of x = -1
That alone is sufficient to dismiss this as a function. If that wasn't bad enough you see that y = -3 and -4 for x = 2
In C we see the same problem
For x = 5 there are two value of y = -3 and -2
So we can disregard C
In B we can see a definite pattern
Between x = -2 and x = 0 we see that y increases by 1 unit for every increase of 1 unit in x. This is a linear relationship with a slope of + 1
Between x = 0 and x = +2, for every increase of 1 unit in the x-value, the y-value decreases by 1 unit. This is also a linear relationship but with a slope of -1
In particular this is what is known as a piecewise function. Its function expression is different for different intervals of x value
It can be expressed as follows
f(x) = x + 2 for -2 ≤ x ≤ 0
= -x + 2 for 0 ≤ x ≤ 2