Find the x and y Intercepts f(x)=1/2 square root of x-3

$f (x) = \frac{1}{2} \sqrt{x - 3}$

Step 1

Find the x-intercepts.

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

$0 = \frac{1}{2} \cdot \sqrt{x - 3}$

Solve the equation.

Rewrite the equation as $\frac{1}{2} \cdot \sqrt{x - 3} = 0$ .

$\frac{1}{2} \cdot \sqrt{x - 3} = 0$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot \sqrt{x - 3}) = 2 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot \sqrt{x - 3})$ .

Combine $\frac{1}{2}$ and $\sqrt{x - 3}$ .

$2 \frac{\sqrt{x - 3}}{2} = 2 \cdot 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{\sqrt{x - 3}}{2} = 2 \cdot 0$

Rewrite the expression.

$\sqrt{x - 3} = 2 \cdot 0$

Simplify the right side.

Multiply $2$ by $0$ .

$\sqrt{x - 3} = 0$

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

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

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 3}$ as ${(x - 3)}^{\frac{1}{2}}$ .

${({(x - 3)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

Simplify ${({(x - 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x - 3)}^{\frac{1}{2}})}^{2}$ .

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

${(x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 3)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(x - 3)}^{1} = 0^{2}$

Simplify.

$x - 3 = 0^{2}$

Simplify the right side.

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = \frac{1}{2} \cdot \sqrt{(0) - 3}$

Simplify $\frac{1}{2} \cdot \sqrt{(0) - 3}$ .

Subtract $3$ from $0$ .

$y = \frac{1}{2} \cdot \sqrt{- 3}$

Rewrite $- 3$ as $- 1 (3)$ .

$y = \frac{1}{2} \cdot \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$y = \frac{1}{2} \cdot (\sqrt{- 1} \cdot \sqrt{3})$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \frac{1}{2} \cdot (i \cdot \sqrt{3})$

Multiply $\frac{1}{2} (i \sqrt{3})$ .

Combine $i$ and $\frac{1}{2}$ .

$y = \frac{i}{2} \sqrt{3}$

Combine $\frac{i}{2}$ and $\sqrt{3}$ .

$y = \frac{i \sqrt{3}}{2}$

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

y-intercept(s): $None$

Step 3

List the intersections.

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

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x)=1/2 square root of x-3

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