Math Problem Statement

Find f(1) for the piecewise-defined function: f(x) = {-5x + 4 if x < 3, -6x - 2 if x ≥ 3}.

Solution

We are given a piecewise-defined function:

\begin{cases} -5x + 4 & \text{if } x < 3 \\ -6x - 2 & \text{if } x \geq 3 \end{cases}$$ To find $$f(1)$$, we need to check which part of the function applies when $$x = 1$$. Since $$1 < 3$$, we use the first part of the function: $$f(x) = -5x + 4$$ Now, substitute $$x = 1$$: $$f(1) = -5(1) + 4 = -5 + 4 = -1$$ So, $$f(1) = -1$$. Would you like any more details or have questions? ### Relative Questions: 1. What is $$f(3)$$ for the same piecewise function? 2. How would the value of $$f(x)$$ change if the condition was $$x > 3$$ instead of $$x \geq 3$$? 3. What happens to $$f(x)$$ as $$x \to -\infty$$? 4. Can a piecewise function be continuous? How does that apply to this function? 5. How would the graph of this function look like? ### Tip: When working with piecewise functions, always ensure you substitute the value of $$x$$ into the correct part of the function based on the given conditions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Piecewise functions
Function evaluation

Formulas

f(x) = -5x + 4 (for x < 3)
f(x) = -6x - 2 (for x ≥ 3)

Theorems

-

Suitable Grade Level

Grades 8-10

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