Which of the following statements isare true about the graph

Which of the following statements is/are true about the graph of the function f(x) = log_2 x? I. The range of f is (-infinity,infinity) II. The x-intercept of the function is (1,0) III. The graph of f is increasing throughout its domain A. I and II only B. I and III only C. II and III only D. I, II, and 111 are all true E. I, II, and III are all false

Solution

y = log2(x)

The function exists for x>0 and it exist for all values of y

So, range of f (- inf , inf)

X intercept : y=0 ; log2(x) =0

x= 2^0 = 1

(1, 0)

Graph is increasing for all values of x

So, Option D all options are true