Math Problem Statement
Evaluate the piecewise function at f(2):
f(x) =
{ x - 2, if x < 3
x + 3, if x >= 3 }
Solution
The image contains a piecewise function defined as:
\begin{cases} x - 2 & \text{if } x < 3 \\ x + 3 & \text{if } x \geq 3 \end{cases}$$ It is asking to find $$f(2)$$, so we'll substitute $$x = 2$$ into the appropriate part of the piecewise function. Since $$2 < 3$$, we use the first part of the function, $$f(x) = x - 2$$: $$f(2) = 2 - 2 = 0$$ Thus, $$f(2) = 0$$. Would you like more details on how piecewise functions work, or have any other questions? Here are 5 related questions to explore: 1. How do you evaluate a piecewise function for multiple values? 2. How can you graph this piecewise function? 3. What is the significance of the boundaries in a piecewise function? 4. Can a piecewise function be continuous at the boundary point? 5. How do piecewise functions model real-world scenarios? **Tip:** When evaluating piecewise functions, always check which condition applies to the input value before substituting into the expression.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Basic Algebra
Formulas
f(x) = x - 2 for x < 3
f(x) = x + 3 for x >= 3
Theorems
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Suitable Grade Level
Grades 9-11