Math Problem Statement

Evaluate the piecewise function at the given values of x for the function f(x) defined as: f(x) = 2x + 5 if x < 0 3x + 6 if x ≥ 0 a) f(-1) b) f(0) c) f(4)

Solution

The image presents a piecewise function f(x)f(x) defined as follows:

\begin{cases} 2x + 5 & \text{if } x < 0 \\ 3x + 6 & \text{if } x \geq 0 \end{cases}$$ You are asked to evaluate $$f(x)$$ at specific values of $$x$$: 1. $$f(-1)$$ 2. $$f(0)$$ 3. $$f(4)$$ ### Solutions: 1. **$$f(-1)$$:** Since $$-1 < 0$$, use the first equation: $$f(x) = 2x + 5$$. $$f(-1) = 2(-1) + 5 = -2 + 5 = 3$$ 2. **$$f(0)$$:** Since $$0 \geq 0$$, use the second equation: $$f(x) = 3x + 6$$. $$f(0) = 3(0) + 6 = 0 + 6 = 6$$ 3. **$$f(4)$$:** Since $$4 \geq 0$$, use the second equation: $$f(x) = 3x + 6$$. $$f(4) = 3(4) + 6 = 12 + 6 = 18$$ ### Final answers: - $$f(-1) = 3$$ - $$f(0) = 6$$ - $$f(4) = 18$$ Let me know if you need further explanations, or if you have any questions! ### Related questions: 1. What is $$f(x)$$ if $$x = -2$$? 2. How would the function behave if we added a third piece for $$x > 5$$? 3. What is the general shape of the graph of this piecewise function? 4. Can you find the value of $$x$$ when $$f(x) = 0$$? 5. What is the slope of the line when $$x \geq 0$$? ### Tip: When working with piecewise functions, always check which condition $$x$$ satisfies before applying the correct equation.

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Algebra

Formulas

f(x) = 2x + 5 for x < 0
f(x) = 3x + 6 for x ≥ 0

Theorems

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Suitable Grade Level

Grades 9-12