Graphing Radical Functions

Domain from the radicand

For an even root, the inside must be at least zero. Set the radicand $\geq 0$ and solve to find the allowed inputs.

For $f(x) = \sqrt{x - 5}$, solve $x - 5 \geq 0$ to get $x \geq 5$. The graph exists only from $x = 5$ rightward.

Starting point and shape

The graph begins where the radicand is zero — the point $(5, 0)$ for $\sqrt{x - 5}$ — and rises slowly to the right.

Odd roots like cube roots have no domain restriction; they accept every real number and extend both directions.

The graph of $y = \sqrt{x + 2}$ below shows the shape: it starts at its endpoint $(-2, 0)$, where the radicand is zero, and curves gently upward to the right, existing only for $x \geq -2$.

Worked examples

Try one yourself

Common questions