Graph g(x)=f(x+2)

$g (x) = f (x + 2)$

Step 1

Rewrite the function as an equation.

$y = f (x + 2)$

Step 2

Simplify $f (x + 2)$ .

Apply the distributive property.

$y = f x + f \cdot 2$

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

$y = f x + 2 f$

Step 3

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 $y = m x + b$ .

$m = 1$

$b = 2 f$

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

Slope: $1$

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

Slope: $1$

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

Step 4

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.

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

Step 5

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

Slope: $1$

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

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

Step 6