Algebra Examples

$f (x) = - \frac{3}{4} x^{- 5}$

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 $x$ .

$0 = - \frac{3}{4} x^{- 5}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- \frac{3}{4} x^{- 5} = 0$ .

$- \frac{3}{4} x^{- 5} = 0$

Step 1.2.2

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3}{4} x^{- 5}) = - \frac{4}{3} \cdot 0$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $- \frac{4}{3} (- \frac{3}{4} x^{- 5})$ .

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Step 1.2.3.1.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{4}{3} (- \frac{3}{4} \cdot \frac{1}{x^{5}}) = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.2

Multiply $\frac{1}{x^{5}}$ by $\frac{3}{4}$ .

$- \frac{4}{3} (- \frac{3}{x^{5} \cdot 4}) = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3

Cancel the common factor of $4$ .

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Step 1.2.3.1.1.3.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3}{x^{5} \cdot 4}) = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3.2

Move the leading negative in $- \frac{3}{x^{5} \cdot 4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3}{x^{5} \cdot 4} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3}{x^{5} \cdot 4} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3.4

Factor $4$ out of $x^{5} \cdot 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3}{4 \cdot x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3.5

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3}{4 \cdot x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.3.6

Rewrite the expression.

$\frac{- 1}{3} \cdot \frac{- 3}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.4

Cancel the common factor of $3$ .

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Step 1.2.3.1.1.4.1

Factor $3$ out of $- 3$ .

$\frac{- 1}{3} \cdot \frac{3 (- 1)}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.4.2

Cancel the common factor.

$\frac{- 1}{3} \cdot \frac{3 \cdot - 1}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.4.3

Rewrite the expression.

$- \frac{- 1}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.5

Move the negative in front of the fraction.

$- - \frac{1}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.6

Multiply $- - \frac{1}{x^{5}}$ .

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Step 1.2.3.1.1.6.1

Multiply $- 1$ by $- 1$ .

$1 \frac{1}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.1.1.6.2

Multiply $\frac{1}{x^{5}}$ by $1$ .

$\frac{1}{x^{5}} = - \frac{4}{3} \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $- \frac{4}{3} \cdot 0$ .

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Step 1.2.3.2.1.1

Multiply $0$ by $- 1$ .

$\frac{1}{x^{5}} = 0 (\frac{4}{3})$

Step 1.2.3.2.1.2

Multiply $0$ by $\frac{4}{3}$ .

$\frac{1}{x^{5}} = 0$

Step 1.2.4

Set the numerator equal to zero.

$1 = 0$

Step 1.2.5

Since $1 \neq 0$ , there are no solutions.

No solution

Step 1.3

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

x-intercept(s): $None$

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 $y$ .

$y = - \frac{3}{4} \cdot {(0)}^{- 5}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - \frac{3}{4} \cdot 0^{- 5}$

Step 2.2.2

Remove parentheses.

$y = - \frac{3}{4} \cdot {(0)}^{- 5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify $- \frac{3}{4} \cdot {(0)}^{- 5}$ .

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Step 2.2.3.1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - \frac{3}{4} \cdot \frac{1}{0^{5}}$

Step 2.2.3.1.2

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

$y = - \frac{3}{4} \cdot \frac{1}{0}$

Step 2.2.3.2

The equation cannot be solved because it is undefined.

$Undefined$

Step 2.3

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): $None$

y-intercept(s): $None$

Step 4