For the function $f$ whose graph is given, which of the following best describes the domain of $f$?

• A. All real numbers $x$ such that $x>0$
• B. All real numbers $x$ such that $x\ne -1$
• C. All real numbers $x$ such that $x\ne 2$
• D. All real numbers $x$

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of the domain of a function. The domain of a function is the set of all possible input values (x-values) for which the function is defined. If there are any restrictions, such as division by zero or square roots of negative numbers, these values are excluded from the domain.
2. Step 2: Analyze the graph of the function f provided in the problem. Look for any points where the function is undefined, such as vertical asymptotes or holes in the graph.
3. Step 3: Identify the x-values where the function is undefined. For example, if the graph has a vertical asymptote at x = -1 or x = 2, these values are excluded from the domain.
4. Step 4: Based on the graph, determine the correct description of the domain. If the function is undefined at specific x-values, the domain will exclude those values. For example, if the function is undefined at x = -1 and x = 2, the domain would be all real numbers except x = -1 and x = 2.
5. Step 5: Write the domain in mathematical notation. For example, if the domain excludes x = -1 and x = 2, it can be written as: {x ∈ ℝ | x ≠ -1, x ≠ 2}. This notation means all real numbers except -1 and 2.