Question

What is the domain and range of |x-3|-5

Answer 1

Domain means all valid values of X. With Absolute values any value of x is valid therefore the domain is: x = all real numbers
Range is all values that can be obtained using the full domain. lets look at what happens if X is 0
\[\left| 0 - 3 \right| -5 = 3 -5 = -2 \]
if x is 3 \[\left| 3 - 3 \right| -5 = 0 -5 = -5 \] this is the lowest value that can be obtained because abs(x - 3) can only be 0 or larger so the range of the equation is \[[ -5 , \infty)\]

Answer 2

Thank you so much!