Which statement correctly describes the domain of a function?

Which statement correctly describes the domain of a function?

• A. All x-values on the graph.
• B. All x-values for which the function is defined.
• C. All y-values produced by the function.
• D. The maximum y-value.

Answer: (B)

The domain is the set of input values for which the function is defined. In other words, these are the x-values you can plug into the function so the expression makes sense (no negative numbers under even roots, no division by zero, arguments of logs positive, etc.). The domain captures all permissible inputs, and any restriction from the formula (like x ≠ 0 in a denominator or x ≥ 0 under a square root) trims away the invalid x-values. Think of the graph: for every x in the domain, there is a corresponding point (x, f(x)) on the graph. The set of x-coordinates that actually appear on the graph matches the domain, while the y-values produced are the range. The other statements pull in a different direction: the range is all the y-values the function outputs, and a maximum y-value concerns that range, not the inputs.

The domain is the set of input values for which the function is defined. In other words, these are the x-values you can plug into the function so the expression makes sense (no negative numbers under even roots, no division by zero, arguments of logs positive, etc.). The domain captures all permissible inputs, and any restriction from the formula (like x ≠ 0 in a denominator or x ≥ 0 under a square root) trims away the invalid x-values.

Think of the graph: for every x in the domain, there is a corresponding point (x, f(x)) on the graph. The set of x-coordinates that actually appear on the graph matches the domain, while the y-values produced are the range.

The other statements pull in a different direction: the range is all the y-values the function outputs, and a maximum y-value concerns that range, not the inputs.