Algebra Examples

f (x) = \sqrt{x}

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

Step 1

Find the domain for

\sqrt{x}

$\sqrt{x}$ .

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Step 1.1

Set the radicand in

\sqrt{x}

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

0

$0$ to find where the expression is defined.

x \geq 0

$x \geq 0$

Step 1.2

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

[0, \infty)

$[0, \infty)$

Set-Builder Notation:

{x | x \geq 0}

${x | x \geq 0}$

Interval Notation:

[0, \infty)

$[0, \infty)$

Set-Builder Notation:

{x | x \geq 0}

${x | x \geq 0}$

Step 2

To find the square root end point, substitute the

x

$x$ value

0

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

\sqrt{x}

$\sqrt{x}$ .

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Step 2.1

Replace the variable

x

$x$ with

0

$0$ in the expression.

f (0) = \sqrt{0}

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

Step 2.2

Simplify the result.

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Step 2.2.1

Remove parentheses.

f (0) = \sqrt{0}

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

Step 2.2.2

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

f (0) = \sqrt{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

$f (0) = 0$

Step 2.2.4

The final answer is

0

$0$ .

y = 0

$y = 0$

y = 0

$y = 0$

y = 0

$y = 0$

Step 3

The square root end point is

(0, 0)

$(0, 0)$ .

(0, 0)

$(0, 0)$

Step 4

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