Math Problem Statement
Evaluate the function for the given values of x. f(x) is a piecewise function defined as: f(x) = -8 if x ≤ -5, f(x) = 0 if -5 < x < 5, and f(x) = 5 if x ≥ 5. Find f(-6) and f(5).
Solution
The piecewise function is given as:
\begin{cases} -8 & \text{if } x \leq -5 \\ 0 & \text{if } -5 < x < 5 \\ 5 & \text{if } x \geq 5 \end{cases}$$ You need to evaluate $$f(x)$$ for $$x = -6$$ and $$x = 5$$. ### For $$x = -6$$: Since $$x = -6$$ is less than or equal to $$-5$$, we use the first condition of the function: $$f(-6) = -8$$ ### For $$x = 5$$: Since $$x = 5$$ is greater than or equal to 5, we use the third condition of the function: $$f(5) = 5$$ Thus, $$f(-6) = -8$$ and $$f(5) = 5$$. ### Correct Answer: The correct option is: $$\boxed{f(-6) = -8 \quad \text{and} \quad f(5) = 5}$$ Do you want further details or have any questions? Here are 5 related questions to expand on this: 1. How would the function behave for values of $$x = 0$$? 2. Can you describe the overall shape of this piecewise function graphically? 3. What is the domain and range of this function? 4. How would you evaluate $$f(x)$$ for $$x = -5$$? 5. What is the limit of $$f(x)$$ as $$x$$ approaches 5 from the left and right? **Tip:** When evaluating piecewise functions, always check which condition of the function applies to your input.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
f(x) = -8 if x ≤ -5, f(x) = 0 if -5 < x < 5, f(x) = 5 if x ≥ 5
Theorems
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Suitable Grade Level
Grades 9-10