I'm assuming that the "linear parent function" is [tex] y = x [/tex]. If so:
A. is true.
In fact, the slope of a line written in the form [tex] y = mx+q [/tex] is [tex]m[/tex], and the line [tex] y = x [/tex] is given by [tex] m=1,\ q=0 [/tex]
C. is true.
Since the origin is the point [tex] (0,0) [/tex], if we compute the function at [tex] x = 0 [/tex], we want [tex] y = 0[/tex]. This is quite trivial since [tex] y = x [/tex]
D. is true.
The domain is affected by denominators (they can be zero), even roots (they don't accept negative inputs) and logarithms (they don't accept non-positive inputs). Since this function has none of these three, the domain is all real numbers.
B. is FALSE.
The range of a function is the set of numbers obtained as output, for all possible inputs. Since, in this case, the input and the output are the same thing, if you give a negative input, you will receive the same negative output. So, the range doesn't consist only of positive numbers.
