Precalculus Examples

$\sqrt{x}$

Step 1

Write $\sqrt{x}$ as an equation.

$y = \sqrt{x}$

Step 2

Find the x-intercepts.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \sqrt{x}$

Solve the equation.

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Rewrite the equation as $\sqrt{x} = 0$ .

$\sqrt{x} = 0$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = 0^{2}$

Simplify each side of the equation.

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

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Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$x^{1} = 0^{2}$

Simplify.

$x = 0^{2}$

Simplify the right side.

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Raising $0$ to any positive power yields $0$ .

$x = 0$

x-intercept(s) in point form.

x-intercept(s): $(0, 0)$

Step 3

Find the y-intercepts.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \sqrt{0}$

Simplify $\sqrt{0}$ .

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Remove parentheses.

$y = \sqrt{0}$

Rewrite $0$ as $0^{2}$ .

$y = \sqrt{0^{2}}$

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

$y = 0$

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 4

List the intersections.

x-intercept(s): $(0, 0)$

y-intercept(s): $(0, 0)$

Step 5