Absolute Value as Piecewise Function
The absolute value function can be written as a piecewise-defined function with two pieces: |x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}. The absolute value function is a classic example of a piecewise-defined function because it has different rules for different input values. When the input is non-negative, the output equals the input. When the input is negative, the output equals the opposite of the input, making the result positive. This skill is part of Grade 11 math in enVision, Algebra 2.
Key Concepts
The absolute value function can be written as a piecewise defined function with two pieces: $$|x| = \begin{cases} x & \text{if } x \geq 0 \\ x & \text{if } x < 0 \end{cases}$$.
Common Questions
What is Absolute Value as Piecewise Function?
The absolute value function can be written as a piecewise-defined function with two pieces: |x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}.
How does Absolute Value as Piecewise Function work?
Example: Using the piecewise definition to evaluate |5|: Since 5 \geq 0, we use the first piece, so |5| = 5.
Give an example of Absolute Value as Piecewise Function.
Using the piecewise definition to evaluate |-3|: Since -3 < 0, we use the second piece, so |-3| = -(-3) = 3.
Why is Absolute Value as Piecewise Function important in math?
The absolute value function is a classic example of a piecewise-defined function because it has different rules for different input values. When the input is non-negative, the output equals the input.
What grade level covers Absolute Value as Piecewise Function?
Absolute Value as Piecewise Function is a Grade 11 math topic covered in enVision, Algebra 2 in Chapter 1: Linear Functions and Systems. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.
What are typical Absolute Value as Piecewise Function problems?
Using the piecewise definition to evaluate |5|: Since 5 \geq 0, we use the first piece, so |5| = 5.; Using the piecewise definition to evaluate |-3|: Since -3 < 0, we use the second piece, so |-3| = -(-3) = 3.; To simplify |2x - 6| when x = 1: First substitute to get |2(1) - 6| = |-4|. Since -4 < 0, we use the second piece: |-4| = -(-4) = 4.