Can someone please verify if my understanding is correct?
This is Q2 of the PrepSwift exercise from the topic Domain & Range of Functions.
Option A&B are easy to understand.
For option C, it’s either an upward or downward parabola. If a parabola has a minimum → values below it are impossible → range is restricted
For option D, it’s a V-shaped graph → has a minimum → cannot take values below that point, therefore, the range is restricted.
This is the reason why Domain is not equal to the range.
It’s decent
f(x) = k/x, k is nonzero
Domain: All real numbers except 0 (b/c we can’t plug in zero into the denominator)
Range: All real numbers except 0 (if k is nonzero, then k/x must be nonzero since x is nonzero).
f(x) = mx+c, m is nonzero
Domain: All real numbers (no restrictions)
Range: All real numbers (plot any non-horizontal (m is nonzero) and non-vertical line (not a function) and you will see that any y value can be achieved)
f(x) = ax^2+bx+c
Domain: All real numbers (no restrictions)
Range: Either all numbers greater than or equal to minimum y value (if a > 0) or all numbers less than or equal to maximum y value (if a < 0)
f(x) = |x| + k
Similar reasoning to quadratic
