Precalculus Examples

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

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 $x$ .

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

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$x - 2 = 0$

Step 1.2.2

Add $2$ to both sides of the equation.

$x = 2$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

$y = \frac{0 - 2}{0^{2} - 2 \cdot 0 - 3}$

Step 2.2.3

Remove parentheses.

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

Step 2.2.4

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

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Step 2.2.4.1

Subtract $2$ from $0$ .

$y = \frac{- 2}{0^{2} - 2 \cdot 0 - 3}$

Step 2.2.4.2

Simplify the denominator.

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Step 2.2.4.2.1

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

$y = \frac{- 2}{0 - 2 \cdot 0 - 3}$

Step 2.2.4.2.2

Multiply $- 2$ by $0$ .

$y = \frac{- 2}{0 + 0 - 3}$

Step 2.2.4.2.3

Add $0$ and $0$ .

$y = \frac{- 2}{0 - 3}$

Step 2.2.4.2.4

Subtract $3$ from $0$ .

$y = \frac{- 2}{- 3}$

Step 2.2.4.3

Dividing two negative values results in a positive value.

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{2}{3})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{2}{3})$

Step 4