Final answer:
The formula for the function graphed on the right is
Explanation:
The graph represents the absolute value function, denoted as
The absolute value function returns the positive magnitude of a given number, regardless of its sign. It's characterized by a "V" shape, centered at the origin (0, 0) on a coordinate plane. The function outputs the absolute distance of any input x from zero, resulting in non-negative values. When x is positive or zero, the output is the same as x . For negative x , the function reflects these values to their positive counterpart, resulting in a mirror image across the x-axis. This behavior leads to a symmetrical graph. The graph increases linearly for positive \( x \) values and decreases linearly for negative x values, maintaining a consistent slope of 1.
The absolute value function has applications in various fields, including mathematics, physics, and engineering, where modeling distances, magnitudes, or differences between values is essential. It's a fundamental function used in solving equations involving real numbers. Understanding its graph and behavior aids in solving inequalities and absolute value equations.