Question

1. State the domain, range, intercept(s) and asymptote(s) of the following:
y= -3sqrt (x-4) - 2

Answer 1

y = -3√(x-4) - 2

domain : x-4 ≥ 0
x ≥ 4

range:
√(x-4) is always positive
then -3√(x-4) is always negative with -3 as its largest value, and so
y ≤ -5

for x-intercept, let y = 0
0 = -3√(x-4) - 2
3√(x-4) = -2/3, not possible, so no x-intercept

for y-intercept, let x = 0
y = -3√-4 - 2, which is undefined, so no y-intercept

No vertical or horizontal asymtotes
There is a curved asymtpote of y = -3√x