Math Problem Statement
The given piecewise function is defined as follows:
1. f(x) = x^2 for x ≤ 2
2. f(x) = 8 - 2x for 2 < x < 4
3. f(x) = 4 for x ≥ 4.
Solution
The given piecewise function in the image is:
x^2, & \text{for } x \leq 2, \\ 8 - 2x, & \text{for } 2 < x < 4, \\ 4, & \text{for } x \geq 4. \end{cases}$$ Would you like help with solving a particular problem related to this function, such as finding its domain, evaluating specific values, or analyzing its continuity? Here are five related questions: 1. What is the domain and range of the given piecewise function $$f(x)$$? 2. Is $$f(x)$$ continuous at $$x = 2$$ and $$x = 4$$? 3. How do you find the limit of $$f(x)$$ as $$x$$ approaches 2 from the left and right? 4. How do you graph this piecewise function? 5. What are the values of $$f(x)$$ at $$x = 1, 3, 5$$? **Tip:** When analyzing a piecewise function, always check the function's behavior at the boundary points where the pieces change.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Continuity
Limits
Formulas
f(x) = x^2 for x ≤ 2
f(x) = 8 - 2x for 2 < x < 4
f(x) = 4 for x ≥ 4
Theorems
Piecewise Function Continuity Theorem
Limit Theorems for Piecewise Functions
Suitable Grade Level
Grades 10-12