Question

what is the domain of the function?

\\(x < 0\\)
\\(x > 0\\)
\\(x < 1\\)
all real numbers

Explanation:

Identify the horizontal boundary of the graph

The graph is a logarithmic curve that approaches the vertical line \(x = 0\) (the y-axis) as an asymptote on the left, but never touches or crosses it.

Determine the interval of x-values

The curve exists only to the right of the y-axis, meaning the function is defined for all real numbers \(x\) that are strictly greater than \(0\).

State the domain inequality

The set of all valid input values is represented by the inequality \(x > 0\).

Answer:

• (A) \(x < 0\)
• (B) \(x > 0\) (Correct answer)
• (C) \(x < 1\)
• (D) all real numbers