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

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

Find the x-intercepts.

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

$0 = 3 \sqrt{x - 1}$

Solve the equation.

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

$3 \sqrt{x - 1} = 0$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $3 {(x - 1)}^{\frac{1}{2}}$ .

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

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

$9 {({(x - 1)}^{\frac{1}{2}})}^{2} = 0^{2}$

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

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

$9 {(x - 1)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(x - 1)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

$9 {(x - 1)}^{1} = 0^{2}$

Simplify.

$9 (x - 1) = 0^{2}$

Apply the distributive property.

$9 x + 9 \cdot - 1 = 0^{2}$

Multiply $9$ by $- 1$ .

$9 x - 9 = 0^{2}$

Simplify the right side.

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

$9 x - 9 = 0$

Solve for $x$ .

Add $9$ to both sides of the equation.

$9 x = 9$

Divide each term in $9 x = 9$ by $9$ and simplify.

Divide each term in $9 x = 9$ by $9$ .

$\frac{9 x}{9} = \frac{9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{9}{9}$

Divide $x$ by $1$ .

$x = \frac{9}{9}$

Simplify the right side.

Divide $9$ by $9$ .

$x = 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Find the y-intercepts.

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

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

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

Subtract $1$ from $0$ .

$y = 3 \sqrt{- 1}$

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

$y = 3 i$

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

y-intercept(s): $None$

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $None$

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

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