For a function on a stated domain, every vertical line $x=a$ with $a$ in that domain must meet t

Question

For a function on a stated domain, every vertical line $x=a$ with $a$ in that domain must meet the graph exactly once. A graph is single-valued if no vertical line meets it more than once.

Determine whether the following mappings are functions:

$ \mathrm{f} (x) = x^{2} + 1 ; x \in \mathbb{R}$
$ \mathrm{h}(x) =\pm \sqrt{x + 1} ; x \in \mathbb{R}, x \ge 0$
$ \mathrm{g} (x) = \sqrt{x + 3} ; x > 2$

Accepted Answer

(a) $f$ is a function. (b) $h$ is not a function. (c) $g$ is a function.

Vertical Line Test

Vertical Line Test

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