f(x) = 1 - ln (x-2) a. What is the domain of f? , b. what is the range of f?, c. what are the x-intercepts of the graph of f?,
Given `f(x)=1-ln(x-2)` :
(a) The base function is `lnx` . This function has been reflected across the x-axis (the negative coefficient), translated 2 units to the right and one unit up.
(b) The domain of `lnx` is `x>0` or `(0,oo)` . Reflecting the graph and translating up did not change the domain, but translating to the right changed the domain to x>2 or `(2,oo)`
(c) The range of `lnx` is all real numbers, and the range of the transformed function is still all real numbers.
(d) The x-intercept of `lnx` is 1. Reflecting across the x-axis does not change the x-intercept. But the horizontal and vertical translations do change the intercept.