Piecewise and Absolute Value Functions
Master key concepts for evaluating, graphing, and solving problems with piecewise and absolute value functions.
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Questions Covered in This Set
10 cards to master
What is a piecewise function?
A function defined by different formulas on different parts of its domain, using different rules depending on the input value.
How do you evaluate a piecewise function for a given input?
Determine which piece (domain interval) the input falls into, then use the corresponding formula for that piece.
Write the absolute value function |x| as a piecewise function.
|x| = x if x ≥ 0, and |x| = -x if x < 0
What does the graph of y = |x| look like?
A V-shape with the vertex at the origin, forming two rays that meet at (0,0).
How do you solve |A| = B where B ≥ 0?
Set up two cases: A = B or A = -B, then solve both equations.
What if an absolute value equation equals a negative number, like |x + 3| = -5?
The equation has no solution because absolute values are never negative.
How do you solve |A| < B where B > 0?
Solve the compound inequality -B < A < B (values between -B and B).
How do you solve |A| > B where B > 0?
Solve A < -B or A > B (values outside the interval from -B to B).
In the function f(x) = a|x - h| + k, what does (h, k) represent?
The vertex of the absolute value function.
When graphing piecewise functions, how do you indicate included vs. excluded endpoints?
Use closed circles for included endpoints and open circles for excluded endpoints.
