Precalculus Examples

$f (x) = \frac{1 - 3 x}{1 - x}$

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 $x$ .

$0 = \frac{1 - 3 x}{1 - x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$1 - 3 x = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Subtract $1$ from both sides of the equation.

$- 3 x = - 1$

Step 1.2.2.2

Divide each term in $- 3 x = - 1$ by $- 3$ and simplify.

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Step 1.2.2.2.1

Divide each term in $- 3 x = - 1$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 1}{- 3}$

Step 1.2.2.2.2

Simplify the left side.

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Step 1.2.2.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 1}{- 3}$

Step 1.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 1}{- 3}$

Step 1.2.2.2.3

Simplify the right side.

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Step 1.2.2.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{1}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{3}, 0)$

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 $y$ .

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

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

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

Step 2.2.2

Simplify $\frac{1 - 3 \cdot 0}{1 - (0)}$ .

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Step 2.2.2.1

Simplify the numerator.

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Step 2.2.2.1.1

Multiply $- 3$ by $0$ .

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

Step 2.2.2.1.2

Add $1$ and $0$ .

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

Step 2.2.2.2

Simplify the denominator.

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Step 2.2.2.2.1

Multiply $- 1$ by $0$ .

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

Step 2.2.2.2.2

Add $1$ and $0$ .

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

Step 2.2.2.3

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): $(\frac{1}{3}, 0)$

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

Step 4