Question

Identify the characteristics of the logarithmic function below. If a value is a non-integer then type it as a reduced fraction: f(x)=log_3(15-5x)+6The domain is AnswerThe range is AnswerThe vertical asymptote is x=Answer

Answer 1

Explanation:

Case: A logarithmic equation

Given:

Required: To find

A) The domain

B) The range

C) The vertical line of asymptote

Method:

A) The domain: The domain is obtained on the x-axis. It includes all applicable vales of x for the graph.

To solve for the domain:

We check for the possible values of x where the log function part is greater than 0

B) The range of the function f(x) is given as:

C) The vertical asymptote is at x= 3 i.e where the graph does not go beyond towards the x-axis

Final answer:

A) The domain are all real values less than 3

B) The range is all real numbers greater than 6

C) The vertical asymptote is at x= 3

Answer 2

Case: A logarithmic equation

Given:

`f(x)=log_3(15-5x)\text{ +6}`

Required: To find

A) The domain

B) The range

C) The vertical line of asymptote

Method:

A) The domain: The domain is obtained on the x-axis. It includes all applicable vales of x for the graph.

To solve for the domain:

We check for the possible values of x where the log function part is greater than 0

`\begin{gathered} (15-5x)>0 \\ 15-5x>0 \\ 15-5x>0 \\ 15>5x \\ \text{Dividing through by 5} \\ 3>x \\ x<3 \end{gathered}`

B) The range of the function f(x) is given as:

`\begin{gathered} \text{Range:} \\ \lbrack f(x)\colon\text{ f(x)>6}\rbrack \end{gathered}`

C) The vertical asymptote is at x= 3 i.e where the graph does not go beyond towards the x-axis

Final answer:

A) The domain are all real values less than 3

B) The range is all real numbers greater than 6

C) The vertical asymptote is at x= 3