Math Problem Statement
Evaluate
f(−9), f(0),
and
f(6)
for the piecewise defined function.
f(x) =
x + 2
if x < 0
1 − x
if x ≥ 0 find f(−9)
Solution
We are given a piecewise-defined function , defined as follows:
\begin{cases} x + 2 & \text{if } x < 0 \\ 1 - x & \text{if } x \geq 0 \end{cases}$$ We need to evaluate $$f(-9)$$, $$f(0)$$, and $$f(6)$$. ### Evaluating $$f(-9)$$: Since $$-9 < 0$$, we use the first piece of the function: $$f(x) = x + 2.$$ Substituting $$x = -9$$: $$f(-9) = -9 + 2 = -7.$$ ### Evaluating $$f(0)$$: Since $$0 \geq 0$$, we use the second piece of the function: $$f(x) = 1 - x.$$ Substituting $$x = 0$$: $$f(0) = 1 - 0 = 1.$$ ### Evaluating $$f(6)$$: Since $$6 \geq 0$$, we use the second piece of the function: $$f(x) = 1 - x.$$ Substituting $$x = 6$$: $$f(6) = 1 - 6 = -5.$$ ### Final Answers: - $$f(-9) = -7$$ - $$f(0) = 1$$ - $$f(6) = -5$$ Let me know if you would like any further clarification! ### Related Questions: 1. What is a piecewise function? 2. How do you determine which piece of a piecewise function to use? 3. Can a piecewise function be continuous at the point where the pieces meet? 4. How do you graph a piecewise function? 5. What is the significance of piecewise functions in real-life scenarios? **Tip:** When working with piecewise functions, always check the domain condition carefully to determine which rule to apply for the given value of $$x$$.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise functions
Formulas
-
Theorems
-
Suitable Grade Level
Grades 10-12