<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-domain-range-of-functions">Domain & Range of Functions Exercise</a></span></p><p>The <span style="color:#27ae60;">Domain</span> of a function refers to ALL possible input, or $x$, values. </p>
<p><strong><span style="color:#8e44ad;">Example 1</span></strong></p>
<p>$$f(x) = x-3$$</p>
<p>In the above case, we can input any $x$ value we want: positive, negative, zero, rational numbers, irrational numbers, etc. So we say the domain is All Real Numbers.</p>
<p><strong><span style="color:#8e44ad;">Example 2</span></strong></p>
<p>$$f(x) = \sqrt{x}$$</p>
<p>In this case, we CANNOT input any $x$ value we want. In fact, we cannot input negative $x$ values. So the domain is $x \geq 0$.</p>
<hr />
<p>The <span style="color:#27ae60;">Range </span>of a function refers to ALL possible output, or $f(x)$, values.</p>
<p><strong><span style="color:#8e44ad;">Example 1</span></strong></p>
<p>$$f(x) = x^2$$</p>
<p>In the above case, we can only get non-negative values for the output because of the squared term $x^2$. So in this case the range is $f(x) \geq 0$.</p>
<p><strong><span style="color:#8e44ad;">Example 2</span></strong></p>
<p>$$f(x) = \frac{1}{x}$$</p>
<p>In this case, we can make the output equal anything EXCEPT $0$ because we cannot divide by $0$. So the range is All Real Numbers except $0$.</p>