answer: the third option, f(x) = 3x
work: since f(X) = y, let's look at the relationships between x and y. the two points we are given are (-2, -6) and (2,6). now, let's compare these to the options we are given.
option one: f(x) = x this is saying that the value of x is equal to the value of y. is 6 equal to 2? no, so this option is incorrect.
option two: f(x) = -x this is saying that the value of y is the value of x, but with the opposite negative/positive sign. are 2 and 6 the same numbers, just one is poistive and one is negative? no. so this option is incorrect.
option three: f(x) = 3x this is saying that the value of y is three times the value of x. is three times 2 equal to 6? yes, it is. is three times -2 equal to -6? yes, iyt is. so this option is correct.
we don't even need to look at number four now, since we know three is the correct answer, and anyways, -2 times 2 is -4,, and not 6.
hope this helps and have a great day!
