Precalculus Examples

$y = \sqrt{16 - x^{2}}$

Step 1

Simplify $\sqrt{16 - x^{2}}$ .

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$y = \sqrt{4^{2} - x^{2}}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x$ .

$y = \sqrt{(4 + x) (4 - x)}$

Step 2

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = \sqrt{(4 + x) (4 - x)}$