Precalculus Examples

$f (x) = \frac{1}{2} x + 3$

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 $x$ .

$0 = \frac{1}{2} x + 3$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{2} x + 3 = 0$ .

$\frac{1}{2} x + 3 = 0$

Step 1.2.2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + 3 = 0$

Step 1.2.3

Subtract $3$ from both sides of the equation.

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

Step 1.2.4

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot - 3$

Step 1.2.5

Simplify both sides of the equation.

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Step 1.2.5.1

Simplify the left side.

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Step 1.2.5.1.1

Cancel the common factor of $2$ .

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Step 1.2.5.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot - 3$

Step 1.2.5.1.1.2

Rewrite the expression.

$x = 2 \cdot - 3$

$x = 2 \cdot - 3$

$x = 2 \cdot - 3$

Step 1.2.5.2

Simplify the right side.

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Step 1.2.5.2.1

Multiply $2$ by $- 3$ .

$x = - 6$

$x = - 6$

$x = - 6$

$x = - 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0)$

x-intercept(s): $(- 6, 0)$

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 $y$ .

$y = \frac{1}{2} \cdot (0) + 3$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $\frac{1}{2}$ by $0$ .

$y = \frac{1}{2} \cdot 0 + 3$

Step 2.2.2

Remove parentheses.

$y = \frac{1}{2} \cdot (0) + 3$

Step 2.2.3

Simplify $\frac{1}{2} \cdot (0) + 3$ .

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Step 2.2.3.1

Multiply $\frac{1}{2}$ by $0$ .

$y = 0 + 3$

Step 2.2.3.2

Add $0$ and $3$ .

$y = 3$

$y = 3$

$y = 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $(- 6, 0)$

y-intercept(s): $(0, 3)$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$