Understanding Piecewise-Defined Function
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Beginner
Start here! Easy to understand
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Beginner Explanation
Piecewise functions can be understood as several smaller functions stitched together.
Practice Problems
Test your understanding with practice problems
1
Quick Quiz
Single Choice Quiz
Beginner
What is the value of the function at $x = -1$ for $y = \begin{cases} x+2, & x < 0 \\ 2, & 0 \leq x \leq 1 \\ -x+3, & x > 1 \end{cases}$?
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2
Real-World Problem
Question Exercise
Intermediate
Teenager Scenario
Imagine a rollercoaster ride where the speed varies: $v = \begin{cases} 10, & t < 10 \\ 20, & 10 \leq t < 20 \\ 15, & t \geq 20 \end{cases}$. Calculate the speed at $t = 15$.
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Consider the function $y = \begin{cases} \frac{x^2}{2}, & x < -2 \\ 0, & -2 \leq x < 2 \\ \frac{x^2}{2}, & x \geq 2 \end{cases}$. Describe the key features of this function.
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4
Challenge Quiz
Single Choice Quiz
Advanced
What is the domain of the function: $y = \begin{cases} \log(x), & 0 < x < 1 \\ \frac{1}{x-2}, & x \geq 1 \end{cases}$?
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