Describe how the graph of the following function can be obtained from one of the basic graphs. \( g(x)=|3 x| \) To obtain the graph of \( g(x)=|3 x| \), start with the graph of \( y= \) by dividing each by it

To obtain the graph of the function \( g(x) = |3x| \) from a basic graph, we can start with the graph of the basic absolute value function, which is \( y = |x| \). Here are the steps to transform the graph of \( y = |x| \) into the graph of \( g(x) = |3x| \): 1. **Start with the basic graph**: Begin with the graph of \( y = |x| \). This is a V-shaped graph that opens upwards, with its vertex at the origin (0, 0). 2. **Horizontal Scaling**: The function \( g(x) = |3x| \) involves a horizontal scaling. The factor of 3 inside the absolute value indicates that we will compress the graph horizontally by a factor of \( \frac{1}{3} \). This means that for every point \( (x, y) \) on the graph of \( y = |x| \), the corresponding point on the graph of \( g(x) \) will be \( \left(\frac{x}{3}, y\right) \). 3. **Resulting Graph**: After applying this horizontal compression, the new graph will still be V-shaped and will open upwards, but it will be narrower than the original graph of \( y = |x| \). The vertex remains at the origin (0, 0). In summary, to obtain the graph of \( g(x) = |3x| \) from the graph of \( y = |x| \), you compress the graph horizontally by a factor of \( \frac{1}{3} \).