Find the domain xintercept and vertical asymptote of the log

Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph. h(x) = log_3 (x - 1) Domain: (0, infinity) (1, infinity) (-infinity, 0) [1, infinity) [0, infinity) (-infinity, 0] x-intercept (x, y) = vertical asymptote x =

Solution

h(x) = log3(x-1)

Domain : (x-1)>0

x>1 ; ( 1, inf)

range : ( - inf , inf)

Vertical asymtote : x =1

x intercept : log3(x-1) =0

(x-1) = 1

x= 2

(2, 0)