Find the x and y Intercepts f(x) = square root of x-3

$f (x) = \sqrt{x} - 3$

Step 1

Find the x-intercepts.

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

$0 = \sqrt{x} - 3$

Solve the equation.

Rewrite the equation as $\sqrt{x} - 3 = 0$ .

$\sqrt{x} - 3 = 0$

Add $3$ to both sides of the equation.

$\sqrt{x} = 3$

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

${\sqrt{x}}^{2} = 3^{2}$

Simplify each side of the equation.

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

${(x^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

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

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

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

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

$x^{1} = 3^{2}$

Simplify.

$x = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$x = 9$

x-intercept(s) in point form.

x-intercept(s): $(9, 0)$

Step 2

Find the y-intercepts.

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

$y = \sqrt{0} - 3$

Simplify $\sqrt{0} - 3$ .

Remove parentheses.

$y = \sqrt{0} - 3$

Simplify each term.

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

$y = \sqrt{0^{2}} - 3$

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

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(9, 0)$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts f(x) = square root of x-3

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