Precalculus Examples

$f (x) = 4 x - 1$

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 $x$ .

$0 = 4 x - 1$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $4 x - 1 = 0$ .

$4 x - 1 = 0$

Step 1.2.2

Add $1$ to both sides of the equation.

$4 x = 1$

Step 1.2.3

Divide each term in $4 x = 1$ by $4$ and simplify.

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Step 1.2.3.1

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $4$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{4}, 0)$

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 $y$ .

$y = 4 (0) - 1$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 4 (0) - 1$

Step 2.2.2

Simplify $4 (0) - 1$ .

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Step 2.2.2.1

Multiply $4$ by $0$ .

$y = 0 - 1$

Step 2.2.2.2

Subtract $1$ from $0$ .

$y = - 1$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{4}, 0)$

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

Step 4