Describe how the graph of the following function can be obtained from one of the basic graphs. \( g(x)=|4 x| \) To obtain the graph of \( g(x)=|4 x| \), start with the graph of \( y=\square \) by dividing each it by

To obtain the graph of the function \( g(x) = |4x| \), we can start with the basic graph of \( y = |x| \), which is the absolute value function. Here are the steps to transform the graph of \( y = |x| \) into the graph of \( g(x) = |4x| \): 1. **Start with the basic graph**: Begin with the graph of \( y = |x| \). 2. **Horizontal Scaling**: The function \( g(x) = |4x| \) can be seen as a horizontal scaling of the graph of \( y = |x| \). Specifically, the factor of 4 inside the absolute value indicates that we are compressing the graph horizontally by a factor of 4. To achieve this, we replace \( x \) with \( \frac{x}{4} \) in the basic graph: \[ y = |x| \quad \text{becomes} \quad y = |4 \cdot \frac{x}{4}| = |x| \] 3. **Final Transformation**: The transformation can be summarized as follows: - Start with \( y = |x| \). - Apply the horizontal compression by a factor of 4, which gives us \( y = |4x| \). Thus, the complete transformation can be described as: To obtain the graph of \( g(x) = |4x| \), start with the graph of \( y = |x| \) and compress it horizontally by a factor of 4.