Using the following function g x 23 log2 2 3x a Find the d

Using the following function g (x) = 2-3 log_2 (2 - 3x). a) Find the domain and range. b) Give the vertical and horizontal asymptote. c) Give the intercepts. d) What is the parent function, f(x)? e) Describe the sequence of transformations from the graph of f (x) to the graph of g (x).

Solution

g(x) = 2 -3 log2(2-3x)

a) Domain : 2-3x >0

x< 2/3

( - inf , 2/3)

Range : ( - inf , inf)

c) Intercepts : g(x) = 0

2 -3log2(2-3x) =0

log2(2-3x) =2

2 -3x = 2^2

2-3x = 4

x = -2/3

y intercept : g(0) = 2 -1 = 1

d) Parent function : f(x) = log2(x)