Algebra Examples

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

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 $x$ .

$0 = - \frac{x + 4}{x - 2}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$x + 4 = 0$

Step 1.2.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0)$

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

$y = - \frac{0 + 4}{0 - 2}$

Step 2.2.3

Remove parentheses.

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

Step 2.2.4

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

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Step 2.2.4.1

Cancel the common factor of $(0) + 4$ and $(0) - 2$ .

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Step 2.2.4.1.1

Factor $2$ out of $0$ .

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

Step 2.2.4.1.2

Factor $2$ out of $4$ .

$y = - \frac{2 \cdot 0 + 2 \cdot 2}{(0) - 2}$

Step 2.2.4.1.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 2$ .

$y = - \frac{2 \cdot (0 + 2)}{(0) - 2}$

Step 2.2.4.1.4

Cancel the common factors.

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Step 2.2.4.1.4.1

Factor $2$ out of $0$ .

$y = - \frac{2 \cdot (0 + 2)}{2 (0) - 2}$

Step 2.2.4.1.4.2

Factor $2$ out of $- 2$ .

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

Step 2.2.4.1.4.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot - 1$ .

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

Step 2.2.4.1.4.4

Cancel the common factor.

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

Step 2.2.4.1.4.5

Rewrite the expression.

$y = - \frac{0 + 2}{0 - 1}$

Step 2.2.4.2

Simplify the expression.

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Step 2.2.4.2.1

Add $0$ and $2$ .

$y = - \frac{2}{0 - 1}$

Step 2.2.4.2.2

Subtract $1$ from $0$ .

$y = - \frac{2}{- 1}$

Step 2.2.4.2.3

Divide $2$ by $- 1$ .

$y = - - 2$

Step 2.2.4.2.4

Multiply $- 1$ by $- 2$ .

$y = 2$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $(- 4, 0)$

y-intercept(s): $(0, 2)$

Step 4