Algebra Examples

$f (x) = \frac{1}{2} (2 x - 4)$

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 $x$ .

$0 = \frac{1}{2} \cdot (2 x - 4)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{2} \cdot (2 x - 4) = 0$ .

$\frac{1}{2} \cdot (2 x - 4) = 0$

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (2 x - 4)) = 2 \cdot 0$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Simplify $2 (\frac{1}{2} \cdot (2 x - 4))$ .

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Step 1.2.3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} (2 x) + \frac{1}{2} \cdot - 4) = 2 \cdot 0$

Step 1.2.3.1.1.2

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.2.1

Factor $2$ out of $2 x$ .

$2 (\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot - 4) = 2 \cdot 0$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$2 (\frac{1}{2} (2 x) + \frac{1}{2} \cdot - 4) = 2 \cdot 0$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$2 (x + \frac{1}{2} \cdot - 4) = 2 \cdot 0$

Step 1.2.3.1.1.3

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.3.1

Factor $2$ out of $- 4$ .

$2 (x + \frac{1}{2} \cdot (2 (- 2))) = 2 \cdot 0$

Step 1.2.3.1.1.3.2

Cancel the common factor.

$2 (x + \frac{1}{2} \cdot (2 \cdot - 2)) = 2 \cdot 0$

Step 1.2.3.1.1.3.3

Rewrite the expression.

$2 (x - 2) = 2 \cdot 0$

Step 1.2.3.1.1.4

Apply the distributive property.

$2 x + 2 \cdot - 2 = 2 \cdot 0$

Step 1.2.3.1.1.5

Multiply $2$ by $- 2$ .

$2 x - 4 = 2 \cdot 0$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Multiply $2$ by $0$ .

$2 x - 4 = 0$

Step 1.2.4

Add $4$ to both sides of the equation.

$2 x = 4$

Step 1.2.5

Divide each term in $2 x = 4$ by $2$ and simplify.

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Step 1.2.5.1

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Step 1.2.5.2

Simplify the left side.

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Step 1.2.5.2.1

Cancel the common factor of $2$ .

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Step 1.2.5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Step 1.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Step 1.2.5.3

Simplify the right side.

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Step 1.2.5.3.1

Divide $4$ by $2$ .

$x = 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

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 $y$ .

$y = \frac{1}{2} \cdot (2 (0) - 4)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{1}{2} \cdot (2 (0) - 4)$

Step 2.2.2

Simplify $\frac{1}{2} \cdot (2 (0) - 4)$ .

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Step 2.2.2.1

Simplify the expression.

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Step 2.2.2.1.1

Multiply $2$ by $0$ .

$y = \frac{1}{2} \cdot (0 - 4)$

Step 2.2.2.1.2

Subtract $4$ from $0$ .

$y = \frac{1}{2} \cdot - 4$

Step 2.2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.2.1

Factor $2$ out of $- 4$ .

$y = \frac{1}{2} \cdot (2 (- 2))$

Step 2.2.2.2.2

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot - 2)$

Step 2.2.2.2.3

Rewrite the expression.

$y = - 2$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - 2)$

Step 4