Graph g(x)=f(1/3x)

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

Step 1

Rewrite the function as an equation.

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

Step 2

Remove parentheses.

$y = f (\frac{1}{3}) \cdot x$

Step 3

Simplify $f (\frac{1}{3}) \cdot x$ .

Combine $f$ and $\frac{1}{3}$ .

$y = \frac{f}{3} \cdot x$

Combine $\frac{f}{3}$ and $x$ .

$y = \frac{f x}{3}$

Step 4

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 $y = m x + b$ .

$m = \frac{1}{3}$

$b = 0$

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

Slope: $\frac{1}{3}$

y-intercept: $(0, 0)$

Slope: $\frac{1}{3}$

y-intercept: $(0, 0)$

Step 5

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.

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

Step 6

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

Slope: $\frac{1}{3}$

y-intercept: $(0, 0)$

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

Step 7