Question

Which of the following describe the function

g(x) = log2 (x - 2) – 3.

Choose ALL that apply.

The domain is the set of all real number greater than 2.

The x-intercept = ( 10,0) and there is no y-intercept

Avertical asymptote at x = 2.

There is no x-intercept and the y-intercept = (0,10 ).

The domain is the set of all real numbers less than 2

The graph of g(x) is symmetric to its inverse exponential function over the line y = 0

The graph of g(x) is symmetric to its inverse exponential function I’ve ether like y = x

A vertical asymptote at x = 10

Answer 1

From the plot and from inspection of the equation the following are true

a.) The domain is the set of all real numbers greater than 2

b.) The x-intercept = (10,0) and there is no y-intercept

c.) A vertical asymptote is at x = 2

f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x

Explanation:

The plot of the graph is attached.

From the plot and from inspection of the equation the following are true

a.) The domain is the set of all real numbers greater than 2

b.) The x-intercept = (10,0) and there is no y-intercept

c.) A vertical asymptote is at x = 2

f.) The graph of g(x) is symmetric to its inverse exponential function over the line y = x