Practice Piecewise Function in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A piecewise function is defined by different formulas on different non-overlapping intervals of its domain, with the applicable formula determined by the input value.
A piecewise function is like a rulebook: look up which rule applies to your input value, then use only that rule to compute the output.
Example 1
easyEvaluate f(x) = \begin{cases} x^2 & x < 0 \\ 2x + 1 & x \geq 0 \end{cases} at x = -3, x = 0, and x = 4.
Example 2
mediumDetermine whether f(x) = \begin{cases} x + 1 & x < 2 \\ 3 & x = 2 \\ 2x - 1 & x > 2 \end{cases} is continuous at x = 2.
Example 3
easyGiven g(x) = \begin{cases} -x & x < -1 \\ x^2 & -1 \leq x \leq 2 \\ 5 & x > 2 \end{cases}, evaluate g(-2), g(1), and g(3).
Example 4
hardFind the value of c so that f(x) = \begin{cases} cx + 1 & x \leq 3 \\ x^2 - 2 & x > 3 \end{cases} is continuous at x = 3.