Calculus Examples

$f (x) = \frac{x - 1}{x + 1}$

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 $x$ .

$0 = \frac{x - 1}{x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$x - 1 = 0$

Step 1.2.2

Add $1$ to both sides of the equation.

$x = 1$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Remove parentheses.

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

Step 2.2.3

Remove parentheses.

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

Step 2.2.4

Cancel the common factor of $(0) - 1$ and $(0) + 1$ .

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Step 2.2.4.1

Rewrite $0$ as $- 1 (0)$ .

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

Step 2.2.4.2

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 2.2.4.3

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

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

Step 2.2.4.4

Cancel the common factor.

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

Step 2.2.4.5

Divide $- 1$ by $1$ .

$y = - 1$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4