Math Problem Statement
Evaluate the piecewise defined function at the indicated values. f(x) =
x2 if x < 0 x + 8 if x ≥ 0 f(−4) = f(−3) = f(0) = f(3) = f(4) =
Solution
The given piecewise function is:
\begin{cases} x^2 & \text{if } x < 0 \\ x + 8 & \text{if } x \geq 0 \end{cases}$$ Now let's evaluate $$f(x)$$ for the given values: 1. **$$f(-4)$$:** Since $$-4 < 0$$, we use the first piece of the function: $$f(x) = x^2$$. $$f(-4) = (-4)^2 = 16$$ 2. **$$f(-3)$$:** Since $$-3 < 0$$, we again use the first piece of the function: $$f(x) = x^2$$. $$f(-3) = (-3)^2 = 9$$ 3. **$$f(0)$$:** Since $$0 \geq 0$$, we use the second piece of the function: $$f(x) = x + 8$$. $$f(0) = 0 + 8 = 8$$ 4. **$$f(3)$$:** Since $$3 \geq 0$$, we use the second piece of the function: $$f(x) = x + 8$$. $$f(3) = 3 + 8 = 11$$ 5. **$$f(4)$$:** Since $$4 \geq 0$$, we use the second piece of the function: $$f(x) = x + 8$$. $$f(4) = 4 + 8 = 12$$ ### Summary of the values: $$f(-4) = 16, \quad f(-3) = 9, \quad f(0) = 8, \quad f(3) = 11, \quad f(4) = 12$$ Would you like more details on any of the steps or concepts? --- Here are five related questions: 1. What is the domain of this piecewise function? 2. What is the range of this piecewise function? 3. How would you graph this piecewise function? 4. How do you find the derivative of a piecewise function? 5. How can you determine if a piecewise function is continuous? **Tip:** Always pay attention to the conditions of piecewise functions to choose the correct expression to use.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Quadratic Functions
Linear Functions
Formulas
f(x) = x^2 for x < 0
f(x) = x + 8 for x ≥ 0
Theorems
Piecewise Function Definition
Quadratic Function Properties
Suitable Grade Level
Grades 9-11