Describe how the graph of the following function can be obtained from one of the basic graphs. \( g(x)=\left|\frac{1}{3} x\right|-3 \) To obtain the graph of \( g(x)=\left|\frac{1}{3} x\right|-3 \), start with the graph of \( y=\square \) by dividing each \( \square \) it \( \square \) unit(s).

To obtain the graph of the function \( g(x) = \left|\frac{1}{3} x\right| - 3 \), we can start with the basic graph of the absolute value function, which is \( y = |x| \). 1. **Start with the basic graph**: The graph of \( y = |x| \) is a V-shaped graph that opens upwards and has its vertex at the origin (0, 0). 2. **Horizontal Stretch**: The term \( \frac{1}{3} x \) indicates a horizontal stretch of the graph. Specifically, the graph of \( y = |x| \) is stretched horizontally by a factor of 3. This means that for every point on the graph of \( y = |x| \), the x-coordinates are multiplied by 3. The new function after this transformation is \( y = | \frac{1}{3} x | \). 3. **Vertical Shift**: The next step is to apply the vertical shift. The term \( -3 \) indicates that we need to shift the entire graph down by 3 units. This means that every point on the graph of \( y = | \frac{1}{3} x | \) will be moved down 3 units. The final function after this transformation is \( g(x) = | \frac{1}{3} x | - 3 \). In summary, to obtain the graph of \( g(x) = \left|\frac{1}{3} x\right| - 3 \), start with the graph of \( y = |x| \) by stretching it horizontally by a factor of 3 and then shifting it down by 3 units.