Precalculus Examples

f (x) = \sqrt{x}

$f (x) = \sqrt{x}$

Step 1

Find the domain for

$\sqrt{x}$ .

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Step 1.1

Set the radicand in

$\sqrt{x}$ greater than or equal to

$0$ to find where the expression is defined.

$x \geq 0$

Step 1.2

The domain is all values of

$x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 2

To find the square root end point, substitute the

$x$ value

$0$ , which is the terminal value in the domain, into

$\sqrt{x}$ .

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Step 2.1

Replace the variable

$x$ with

$0$ in the expression.

$f (0) = \sqrt{0}$

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

$f (0) = \sqrt{0}$

Step 2.2.2

Rewrite

$0$ as

$0^{2}$ .

$f (0) = \sqrt{0^{2}}$

Step 2.2.3

Pull terms out from under the radical, assuming positive real numbers.

$f (0) = 0$

Step 2.2.4

The final answer is

$0$ .

$y = 0$

Step 3

The square root end point is

$(0, 0)$ .

$(0, 0)$

Step 4

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