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<p>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.</p>
<p>Determine whether the following mappings are functions:</p>
<ol class="abc-list"><li data-list-item-id="item-1761899071239-xlxhjz11s" data-list-item-path="item-1761899071239-xlxhjz11s"><div class="list-item-paragraph">\( \mathrm{f} (x) = x^{2} + 1 ; x \in \mathbb{R}\)</div></li><li data-list-item-id="item-1761899072552-4cnv6w2si" data-list-item-path="item-1761899072552-4cnv6w2si"><div class="list-item-paragraph">\( \mathrm{h}(x) =\pm \sqrt{x + 1} ; x \in \mathbb{R},  x \ge 0\)</div></li><li data-list-item-id="item-1761899073182-ft2vc91yv" data-list-item-path="item-1761899073182-ft2vc91yv"><div class="list-item-paragraph">\( \mathrm{g} (x) = \sqrt{x + 3} ; x &gt; 2\)</div></li></ol>

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:

Vertical Line Test

Functions

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