Math Problem Statement
Evaluate f(-3). The function f(x) is defined as a piecewise function: f(x) = { -x^2 - 4x, if x <= 0; x, if x > 0 }
Solution
The given function is defined as a piecewise function:
\begin{cases} -x^2 - 4x & \text{if } x \leq 0 \\ x & \text{if } x > 0 \end{cases}$$ We are asked to evaluate $$f(-3)$$. Since $$-3 \leq 0$$, we will use the first piece of the function: $$f(x) = -x^2 - 4x \quad \text{for } x \leq 0$$ Substitute $$x = -3$$: $$f(-3) = -(-3)^2 - 4(-3)$$ $$= -(9) + 12 = -9 + 12 = 3$$ Thus, $$f(-3) = 3$$. The correct answer is **3**. Would you like further details or have any questions? Here are 5 related questions for further practice: 1. How would you evaluate $$f(2)$$ for the given function? 2. What is the value of $$f(0)$$ in this piecewise function? 3. How does the behavior of the function differ for $$x \leq 0$$ and $$x > 0$$? 4. What are the key characteristics of a piecewise function? 5. Can you find the domain and range of this function? **Tip:** Always pay close attention to which piece of a piecewise function applies based on the input value.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Quadratic Functions
Algebra
Formulas
f(x) = -x^2 - 4x for x <= 0
f(x) = x for x > 0
Theorems
Piecewise Function Definition
Suitable Grade Level
Grades 9-12