Question

Select all the correct answers.Consider the graph of the function (=) = log, I.Y443212X0246810-1-1-27What are the features of function gif g(x) = -f(1) - 120 2021 Edmentum. All rights reserved.

Answer 1

First, find an expression for g(x):

`\begin{gathered} f(x)=\log _2(x) \\ g(x)=-f(x)-1 \\ =-\log _2(x)-1 \end{gathered}`

The x-intercept of g(x) is a number such that g(x)=0. Then:

`\begin{gathered} -\log _2(x)-1=0 \\ \Rightarrow-1=\log _2(x) \\ \Rightarrow\log _2(x)=-1 \\ \Rightarrow x=2^(-1) \\ \Rightarrow x=(1)/(2) \end{gathered}`

Then, the coordinates of the x-intercept are:

`((1)/(2),0)`

The domain of g is the set of all values that x can take. The domain of a logarithm is the set of all positive numbers. Then, the domain of g is:

`(0,\infty)`

The y-intercept is the value of the function when x=0. Since 0 is not in the domain of g, then, g does not have a y-intercept.