Describe how the graph of the following function can be obtained from one of the basic graphs. \( g(x)=\left|\frac{1}{4} x\right|+1 \) To obtain the graph of \( g(x)=\left|\frac{1}{4} x\right|+1 \), start with the graph of \( y=\square \) unit(s).

To obtain the graph of the function \( g(x) = \left|\frac{1}{4} x\right| + 1 \), we can start with the graph of the basic function \( y = |x| \). Here are the steps to transform the graph: 1. **Start with the graph of \( y = |x| \)**: This is a V-shaped graph that opens upwards and has its vertex at the origin (0, 0). 2. **Horizontal Stretch**: The term \( \frac{1}{4} x \) indicates a horizontal stretch of the graph. Specifically, the graph of \( y = |x| \) is stretched horizontally by a factor of 4. This means that for every x-value, the corresponding y-value will be the same, but the x-values will be four times larger. The new graph will still have a V shape, but it will be wider. 3. **Vertical Shift**: The \( +1 \) at the end of the function indicates a vertical shift. After stretching the graph horizontally, we will shift the entire graph of \( y = \left|\frac{1}{4} x\right| \) up by 1 unit. This means that the vertex of the V shape will move from (0, 0) to (0, 1). Putting it all together, the graph of \( g(x) = \left|\frac{1}{4} x\right| + 1 \) can be obtained from the graph of \( y = |x| \) by first stretching it horizontally by a factor of 4 and then shifting it up by 1 unit. So, to summarize: To obtain the graph of \( g(x) = \left|\frac{1}{4} x\right| + 1 \), start with the graph of \( y = |x| \), stretch it horizontally by 4 units, and then shift it up by 1 unit.