Piecewise Function Calculator
Evaluate a piecewise-defined function at x by selecting the matching interval branch.
Inputs
Expression for the first piece
x value where the function switches
Expression for the second piece
f(x)
7.00000000
Branch Used
f₂(x) = 2*x + 1 (x ≥ 0)
Left limit at boundary
0.000000
Right limit at boundary
1.000000
Step by step
Values used
f₁(x) (when x < boundary) = x^2; Boundary value = 0; f₂(x) (when x ≥ boundary) = 2*x + 1; x value to evaluate = 3
Piecewise definition
f(x) = { f₁(x) if x < c ; f₂(x) if x ≥ c }
f(x)
= 7.00000000
Branch Used
= f₂(x) = 2*x + 1 (x ≥ 0)
Left limit at boundary
= 0.000000
Right limit at boundary
= 1.000000
How it works
A piecewise function uses different expressions on different intervals. This calculator evaluates a two-piece function: f₁(x) when x < boundary, and f₂(x) when x ≥ boundary. It also checks the one-sided limits at the boundary to indicate continuity.
Formula
Piecewise definition
f(x) = { f₁(x) if x < c ; f₂(x) if x ≥ c }
- c
- Boundary value
- f₁
- Left branch
- f₂
- Right branch
Frequently Asked Questions
Can I have more than two pieces?
This calculator supports two pieces. For more complex piecewise functions, evaluate each piece separately using the Function Calculator.
How do I check if the function is continuous?
Compare the left limit and right limit at the boundary. If they are equal, the function is continuous at that point.