Math Problem Statement
evaluate f(-3), f(0), and f(2) given f(x) = {5 if x<2, 1/2 x-3 if x>=2
Solution
To evaluate , , and , we first examine the piecewise function:
\begin{cases} 5 & \text{if } x < 2 \\ \frac{1}{2}x - 3 & \text{if } x \geq 2 \end{cases}$$ Now, let's evaluate each case: 1. **Evaluate $$f(-3)$$:** Since $$-3 < 2$$, we use $$f(x) = 5$$: $$f(-3) = 5$$ 2. **Evaluate $$f(0)$$:** Since $$0 < 2$$, we use $$f(x) = 5$$: $$f(0) = 5$$ 3. **Evaluate $$f(2)$$:** Since $$2 \geq 2$$, we use $$f(x) = \frac{1}{2}x - 3$$: $$f(2) = \frac{1}{2}(2) - 3 = 1 - 3 = -2$$ ### Final Results: $$f(-3) = 5, \quad f(0) = 5, \quad f(2) = -2$$ Would you like further details or have any questions? Here are 5 related questions for practice: 1. What is $$f(4)$$ given the same function? 2. For what values of $$x$$ is $$f(x) = 0$$? 3. How would the function change if the condition for $$x \geq 2$$ became $$x > 2$$? 4. What happens to the function if we modify $$f(x) = \frac{1}{2}x - 3$$ to $$f(x) = x - 3$$ for $$x \geq 2$$? 5. Can you sketch the graph of this piecewise function? **Tip:** Always check the condition of a piecewise function before evaluating.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Functions
Inequalities
Formulas
f(x) = 5, for x < 2
f(x) = 1/2 * x - 3, for x >= 2
Theorems
-
Suitable Grade Level
Grades 9-11