Math Problem Statement
Evaluate this function at x=−2. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate "Undefined".
Evaluate this function at x = −2. Express your answer as an integer or simplified fraction. If the function is undefined at the given value, indicate 'Undefined'.
Solution
To evaluate the function at , we'll use the piecewise definition provided in the image:
\begin{cases} -\frac{1}{4}x - 6 & \text{if } x \leq -2 \\ -3x - 3 & \text{if } x > -2 \end{cases}$$ Since $$x = -2$$, we need to use the first part of the piecewise function because $$-2 \leq -2$$. Substituting $$x = -2$$ into the function: $$f(-2) = -\frac{1}{4}(-2) - 6$$ Calculate the expression step by step: $$f(-2) = \frac{1}{2} - 6 = \frac{1}{2} - \frac{12}{2} = \frac{1 - 12}{2} = \frac{-11}{2}$$ Thus, the value of the function at $$x = -2$$ is $$\frac{-11}{2}$$. Would you like more details or have any questions? Here are some related questions you might consider: 1. What is the value of $$f(x)$$ at $$x = 0$$? 2. How would you find the derivative of $$f(x)$$ for $$x \leq -2$$? 3. What is the domain of the function $$f(x)$$? 4. How does the function behave as $$x$$ approaches $$-2$$ from the left and the right? 5. Is the function continuous at $$x = -2$$? Why or why not? **Tip:** When working with piecewise functions, always pay attention to the specific condition for each piece before substituting the value of $$x$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Equations
Formulas
f(x) = -\frac{1}{4}x - 6
f(x) = -3x - 3
Theorems
-
Suitable Grade Level
Grades 9-11