L \( g(x)=\left|\frac{1}{2} x\right|-2 \) To obtain the graph of \( g(x)=\left|\frac{1}{2} x\right|-2 \), start with the graph of \( y=\square \) of the following function can be obtained from one of the basic graphs.

To obtain the graph of \( g(x) = \left|\frac{1}{2} x\right| - 2 \), we can start with the graph of the basic absolute value function, which is \( y = |x| \). Here are the steps to transform the graph: 1. **Horizontal Scaling**: The term \( \frac{1}{2} x \) indicates a horizontal stretch by a factor of 2. This means that for every \( x \) value, the corresponding \( y \) value will be the same as if we were using \( 2x \) instead of \( x \). So, the graph of \( y = |x| \) will be stretched horizontally. 2. **Vertical Shift**: The \( -2 \) at the end indicates a vertical shift downward by 2 units. This means that after applying the horizontal stretch, we will move the entire graph down by 2 units. Putting it all together, we can summarize the transformations as follows: - Start with the graph of \( y = |x| \). - Apply a horizontal stretch by a factor of 2 to get \( y = | \frac{1}{2} x | \). - Shift the graph down by 2 units to obtain \( g(x) = | \frac{1}{2} x | - 2 \). So, the function that can be obtained from one of the basic graphs is \( y = |x| \).