Math Problem Statement
Find f(-6) given the piecewise function: f(x) = { x + 6 for x < -5, -5 for x = -5, -(x + 5)^2 + 1 for x > -5 }.
Solution
We are given a piecewise function and are asked to find .
The piecewise function is defined as:
\begin{cases} x + 6 & \text{for } x < -5 \\ -5 & \text{for } x = -5 \\ -(x + 5)^2 + 1 & \text{for } x > -5 \end{cases}$$ Since $$-6$$ is less than $$-5$$, we use the first piece of the function, $$f(x) = x + 6$$. Now substitute $$x = -6$$ into this expression: $$f(-6) = -6 + 6 = 0$$ Thus, $$f(-6) = 0$$. Would you like more details or explanations on this? Here are some related questions you might find helpful: 1. What is the value of $$f(-5)$$ using the same function? 2. How would you find $$f(0)$$ for this function? 3. What is the behavior of the function at $$x = -5$$? 4. How can you determine whether the function is continuous at $$x = -5$$? 5. What would the graph of this piecewise function look like? **Tip:** When evaluating a piecewise function, always check which condition the given value satisfies before applying the correct expression.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Algebra
Formulas
f(x) = x + 6
f(x) = -5
f(x) = -(x + 5)^2 + 1
Theorems
Substitution for piecewise functions
Suitable Grade Level
Grades 9-11