Math Problem Statement
Evaluate the piecewise function f(x) = {5 if x <= 4, 4x - 6 if x > 4} for f(-5), f(0), f(4), f(5), and f(7).
Solution
This is a piecewise function , where the value of the function depends on whether is less than or equal to 4 or greater than 4. The function is defined as:
5 & \text{if } x \leq 4 \\ 4x - 6 & \text{if } x > 4 \end{cases}$$ Now, let's evaluate the function for each value provided: 1. $$f(-5)$$: Since $$-5 \leq 4$$, use the first case, $$f(x) = 5$$. So, $$f(-5) = 5$$. 2. $$f(0)$$: Since $$0 \leq 4$$, use the first case, $$f(x) = 5$$. So, $$f(0) = 5$$. 3. $$f(4)$$: Since $$4 \leq 4$$, use the first case, $$f(x) = 5$$. So, $$f(4) = 5$$. 4. $$f(5)$$: Since $$5 > 4$$, use the second case, $$f(x) = 4x - 6$$. So, $$f(5) = 4(5) - 6 = 20 - 6 = 14$$. 5. $$f(7)$$: Since $$7 > 4$$, use the second case, $$f(x) = 4x - 6$$. So, $$f(7) = 4(7) - 6 = 28 - 6 = 22$$. The final answers are: $$f(-5) = 5, \quad f(0) = 5, \quad f(4) = 5, \quad f(5) = 14, \quad f(7) = 22$$ Would you like more details on how piecewise functions work or any further clarifications? Here are 5 questions to consider based on this problem: 1. What is a piecewise function, and how do you evaluate it? 2. What are the conditions that determine which part of the function to use? 3. How does the value of $$f(x)$$ change as $$x$$ crosses the boundary at $$x = 4$$? 4. Can you describe a real-world scenario that could be modeled by this kind of function? 5. How would the function change if the condition $$x \leq 4$$ were instead $$x < 4$$? **Tip:** Always check the conditions of a piecewise function carefully before evaluating to ensure you are using the correct rule for each $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = 5 if x <= 4
f(x) = 4x - 6 if x > 4
Theorems
-
Suitable Grade Level
Grades 7-9