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 \( y=\square \) by dividing each

To obtain the graph of the function \( g(x) = |3x| \), we can start with the basic graph of the 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 coefficient of \( x \) inside the absolute value is 3, which means we will compress the graph horizontally by a factor of \( \frac{1}{3} \). - To apply this transformation, for every point \( (x, y) \) on the graph of \( y = |x| \), we will replace \( x \) with \( \frac{x}{3} \). This means that the new points will be \( \left(\frac{x}{3}, y\right) \). 3. **Resulting Graph**: After applying the horizontal compression, the new graph will still be V-shaped, but it will be narrower than the original graph of \( y = |x| \). The vertex remains at the origin (0, 0), but the slopes of the lines forming the V will be steeper. In summary, to obtain the graph of \( g(x) = |3x| \), start with the graph of \( y = |x| \) and compress it horizontally by a factor of \( \frac{1}{3} \).