Algebra Examples

$f (x) = - 2 x^{\frac{1}{4}}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = - 2 x^{\frac{1}{4}}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 2 x^{\frac{1}{4}} = 0$ .

$- 2 x^{\frac{1}{4}} = 0$

Step 1.2.2

Divide each term in $- 2 x^{\frac{1}{4}} = 0$ by $- 2$ and simplify.

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Step 1.2.2.1

Divide each term in $- 2 x^{\frac{1}{4}} = 0$ by $- 2$ .

$\frac{- 2 x^{\frac{1}{4}}}{- 2} = \frac{0}{- 2}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor.

$\frac{- 2 x^{\frac{1}{4}}}{- 2} = \frac{0}{- 2}$

Step 1.2.2.2.2

Divide $x^{\frac{1}{4}}$ by $1$ .

$x^{\frac{1}{4}} = \frac{0}{- 2}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $0$ by $- 2$ .

$x^{\frac{1}{4}} = 0$

Step 1.2.3

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{4}})}^{4} = 0^{4}$

Step 1.2.4

Simplify the exponent.

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Step 1.2.4.1

Simplify the left side.

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Step 1.2.4.1.1

Simplify ${(x^{\frac{1}{4}})}^{4}$ .

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Step 1.2.4.1.1.1

Multiply the exponents in ${(x^{\frac{1}{4}})}^{4}$ .

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Step 1.2.4.1.1.1.1

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

$x^{\frac{1}{4} \cdot 4} = 0^{4}$

Step 1.2.4.1.1.1.2

Cancel the common factor of $4$ .

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Step 1.2.4.1.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = 0^{4}$

Step 1.2.4.1.1.1.2.2

Rewrite the expression.

$x^{1} = 0^{4}$

Step 1.2.4.1.1.2

Simplify.

$x = 0^{4}$

Step 1.2.4.2

Simplify the right side.

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Step 1.2.4.2.1

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

$x = 0$

Step 1.3

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = - 2 {(0)}^{\frac{1}{4}}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - 2 \cdot 0^{\frac{1}{4}}$

Step 2.2.2

Remove parentheses.

$y = - 2 {(0)}^{\frac{1}{4}}$

Step 2.2.3

Simplify $- 2 {(0)}^{\frac{1}{4}}$ .

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Step 2.2.3.1

Simplify the expression.

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Step 2.2.3.1.1

Rewrite $0$ as $0^{4}$ .

$y = - 2 {(0^{4})}^{\frac{1}{4}}$

Step 2.2.3.1.2

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

$y = - 2 \cdot 0^{4 (\frac{1}{4})}$

Step 2.2.3.2

Cancel the common factor of $4$ .

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Step 2.2.3.2.1

Cancel the common factor.

$y = - 2 \cdot 0^{4 (\frac{1}{4})}$

Step 2.2.3.2.2

Rewrite the expression.

$y = - 2 \cdot 0^{1}$

Step 2.2.3.3

Evaluate the exponent.

$y = - 2 \cdot 0$

Step 2.2.3.4

Multiply $- 2$ by $0$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4