1. **State the problem:** We are given the function $$y = \frac{1}{4} |x|$$ and asked to understand its graph and properties. 2. **Formula and explanation:** The absolute value function $$|x|$$ outputs the distance of $$x$$ from zero, always non-negative. Multiplying by $$\frac{1}{4}$$ scales the output vertically by a factor of $$\frac{1}{4}$$, making the graph less steep. 3. **Graph shape:** The graph is V-shaped with the vertex at the origin $$(0,0)$$. 4. **Piecewise form:** We can write the function as $$ y = \begin{cases} \frac{1}{4}x & \text{if } x \geq 0 \\ -\frac{1}{4}x & \text{if } x < 0 \end{cases} $$ 5. **Slope:** The slope of the right arm is $$\frac{1}{4}$$ and the slope of the left arm is $$-\frac{1}{4}$$. 6. **Intercepts:** The vertex at $$(0,0)$$ is the only intercept. 7. **Summary:** The graph is a V-shaped absolute value function centered at the origin with arms extending upward and outward symmetrically, each with slope magnitude $$\frac{1}{4}$$.