Math Problem Statement
Please answer the question or the questions
If k(x) is a piecewise function defined as follows: k(x) = 4 if x < 0, k(x) = x + 8 if 0 ≤ x < 1, and k(x) = 1 - x if x ≥ 1. Find k(-4), k(0), k(1), and k(-0.009).
Solution
We are given the function defined piecewise as follows:
\begin{cases} 4 & \text{if } x < 0 \\ x + 8 & \text{if } 0 \leq x < 1 \\ 1 - x & \text{if } x \geq 1 \end{cases}$$ Let's evaluate the given points: ### (a) $$k(-4)$$ Since $$-4 < 0$$, we use the first part of the piecewise function: $$k(-4) = 4$$ ### (b) $$k(0)$$ Since $$0 \leq 0 < 1$$, we use the second part of the piecewise function: $$k(0) = 0 + 8 = 8$$ ### (c) $$k(1)$$ Since $$1 \geq 1$$, we use the third part of the piecewise function: $$k(1) = 1 - 1 = 0$$ ### (d) $$k(-0.009)$$ Since $$-0.009 < 0$$, we use the first part of the piecewise function: $$k(-0.009) = 4$$ ### Summary of answers: - (a) $$k(-4) = 4$$ - (b) $$k(0) = 8$$ - (c) $$k(1) = 0$$ - (d) $$k(-0.009) = 4$$ Would you like any more details or clarifications on these steps? Here are some follow-up questions: 1. What is a piecewise function, and how do you identify which part to use? 2. How would the function behave for values like $$x = 2$$? 3. Can you explain how the function behaves at the boundaries $$x = 0$$ and $$x = 1$$? 4. What happens if $$x$$ is a decimal between 0 and 1? 5. How does the third part of the piecewise function behave for very large values of $$x$$? **Tip:** When dealing with piecewise functions, always check the domain for each condition to select the correct piece to evaluate.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise functions
Evaluating functions
Formulas
k(x) = 4 if x < 0
k(x) = x + 8 if 0 ≤ x < 1
k(x) = 1 - x if x ≥ 1
Theorems
Piecewise function evaluation
Suitable Grade Level
Grades 10-12