Graph g(x)=-1/2f(x+2)

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

Rewrite the function as an equation.

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

Remove parentheses.

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

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

Apply the distributive property.

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

Move $2$ to the left of $f$ .

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

Apply the distributive property.

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

Multiply $- \frac{1}{2} (f x)$ .

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

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

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $2 f$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = - \frac{x f}{2} - 1 f$

Simplify the expression.

Rewrite $- 1 f$ as $- f$ .

$y = - \frac{x f}{2} - f$

Reorder $x$ and $f$ .

$y = - \frac{f x}{2} - f$

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{2}$

$b = - f$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

y-intercept: $(0, - f)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, - f)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - f \\ 1 & - \frac{3 f}{2} \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $- \frac{1}{2}$

y-intercept: $(0, - f)$

$\begin{array}{c} x & y \\ 0 & - f \\ 1 & - \frac{3 f}{2} \end{array}$

Graph g(x)=-1/2f(x+2)

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