Math Problem Statement
Evaluate f(-3) in the piecewise function below.
Evaluate f(-3) in the piecewise function below.
Solution
To evaluate in the given piecewise function, we need to determine which piece applies for .
The piecewise function is:
\begin{cases} x - 6 & \text{for } x \leq -3 \\ 5 & \text{for } -3 < x \leq 5 \\ -x + 8 & \text{for } x \geq 6 \end{cases}$$ Since $$-3 \leq -3$$, the first condition $$x - 6$$ applies when $$x \leq -3$$. Now, substituting $$x = -3$$ into the first piece: $$f(-3) = -3 - 6 = -9$$ Thus, $$f(-3) = -9$$. Would you like further details, or do you have any questions? Here are 5 related questions for practice: 1. What is $$f(-4)$$? 2. What is $$f(0)$$? 3. What is the value of $$f(6)$$? 4. How would you graph the piecewise function? 5. What is the domain and range of this function? **Tip:** Always check which condition applies before evaluating a piecewise function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = x - 6 for x ≤ -3
f(x) = 5 for -3 < x ≤ 5
f(x) = -x + 8 for x ≥ 6
Theorems
-
Suitable Grade Level
Grades 9-12