Math Problem Statement
evaluate the piecewise function for the given values of x
Evaluate the piecewise function for the given values of x: f(-2), f(6), and f(1).
Solution
The given piecewise function is:
2x + 1 & \text{if } x < 1 \\ -2x + 3 & \text{if } x \geq 1 \end{cases}$$ Now, let's evaluate the function for the given values of $$x$$: 1. $$f(-2)$$: - Since $$-2 < 1$$, we use the first part of the function: $$2x + 1$$. $$f(-2) = 2(-2) + 1 = -4 + 1 = -3$$ So, $$f(-2) = -3$$. 2. $$f(6)$$: - Since $$6 \geq 1$$, we use the second part of the function: $$-2x + 3$$. $$f(6) = -2(6) + 3 = -12 + 3 = -9$$ So, $$f(6) = -9$$. 3. $$f(1)$$: - Since $$1 \geq 1$$, we use the second part of the function: $$-2x + 3$$. $$f(1) = -2(1) + 3 = -2 + 3 = 1$$ So, $$f(1) = 1$$. ### Final Answers: - $$f(-2) = -3$$ - $$f(6) = -9$$ - $$f(1) = 1$$ Would you like more details on any of these evaluations? ### Related Questions: 1. What would $$f(x)$$ be for $$x = 0$$? 2. How would the function change if the inequality for $$x \geq 1$$ was modified to $$x > 1$$? 3. Can the function $$f(x)$$ be continuous at $$x = 1$$? Why or why not? 4. What is the domain and range of $$f(x)$$? 5. How would you graph this piecewise function? ### Tip: For piecewise functions, always pay close attention to the inequalities to determine which part of the function to use for a specific value of $$x$$.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Linear Functions
Formulas
f(x) = 2x + 1 if x < 1
f(x) = -2x + 3 if x ≥ 1
Theorems
-
Suitable Grade Level
Grades 8-10