The equation $y = |2x - 10|$ represents the absolute value function. To better understand this function, we can break it down into two cases based on the definition of absolute value:

Case 1: When $2x - 10 \geq 0$

If the expression inside the absolute value is non-negative, the absolute value simply removes the absolute value bars: $y = 2x - 10$ This occurs when: $2x - 10 \geq 0 \implies x \geq 5$ So, for $x \geq 5$, the function is $y = 2x - 10$.

Case 2: When $2x - 10 < 0$

If the expression inside the absolute value is negative, the absolute value changes the sign of the expression: $y = -(2x - 10) = -2x + 10$ This occurs when: $2x - 10 < 0 \implies x < 5$ So, for $x < 5$, the function is $y = -2x + 10$.

Summary of the piecewise function:

\begin{cases} 2x - 10 & \text{if } x \geq 5 \\ -2x + 10 & \text{if } x < 5 \end{cases}$$ The graph of this function is a V-shape with the vertex at $$(5, 0)$$, and the function is symmetric about the vertical line $$x = 5$$. Would you like a more detailed graph or further explanations? Here are 5 related questions for deeper exploration: 1. What is the slope of each piece of the function? 2. How do you find the vertex of an absolute value function? 3. Can you calculate the y-intercept of this function? 4. How would the function change if the absolute value were removed? 5. How does the function behave as $$x \to \infty$$ and $$x \to -\infty$$? **Tip**: The vertex of an absolute value function occurs where the expression inside the absolute value equals zero.