Precalculus Examples

$f (x) = \frac{3 x + 3}{7 x + 28}$

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 $x$ .

$0 = \frac{3 x + 3}{7 x + 28}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$3 x + 3 = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Subtract $3$ from both sides of the equation.

$3 x = - 3$

Step 1.2.2.2

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

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Step 1.2.2.2.1

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

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

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.

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

Step 1.2.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 1.2.2.2.3

Simplify the right side.

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Step 1.2.2.2.3.1

Divide $- 3$ by $3$ .

$x = - 1$

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 $y$ .

$y = \frac{3 (0) + 3}{7 (0) + 28}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{3 (0) + 3}{7 (0) + 28}$

Step 2.2.2

Simplify $\frac{3 (0) + 3}{7 (0) + 28}$ .

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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 $0$ .

$y = \frac{0 + 3}{7 (0) + 28}$

Step 2.2.2.1.2

Add $0$ and $3$ .

$y = \frac{3}{7 (0) + 28}$

Step 2.2.2.2

Simplify the denominator.

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Step 2.2.2.2.1

Multiply $7$ by $0$ .

$y = \frac{3}{0 + 28}$

Step 2.2.2.2.2

Add $0$ and $28$ .

$y = \frac{3}{28}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{3}{28})$

Step 3

List the intersections.

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

y-intercept(s): $(0, \frac{3}{28})$

Step 4