Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![In this problem, we have a piecewise defined function \( f(x) \):
\[
f(x) =
\begin{cases}
- \frac{1}{4}x - 2 & \text{if } x \neq 2 \\
-1 & \text{if } x = 2
\end{cases}
\]
We need to find the values of the function at specific points: \( f(-2) \), \( f(2) \), and \( f(4) \).
### Calculations:
1. **\( f(-2) \):**
Since \(-2 \neq 2\), use the first case:
\[
f(-2) = -\frac{1}{4}(-2) - 2 = \frac{1}{2} - 2 = -\frac{3}{2}
\]
2. **\( f(2) \):**
Since \(x = 2\), use the second case:
\[
f(2) = -1
\]
3. **\( f(4) \):**
Since \(4 \neq 2\), use the first case:
\[
f(4) = -\frac{1}{4}(4) - 2 = -1 - 2 = -3
\]
### Final Values:
- \( f(-2) = -\frac{3}{2} \)
- \( f(2) = -1 \)
- \( f(4) = -3 \)
The graph or diagrams do not represent any visual content specific to the function but provide interface elements for inputting answers in an educational tool. The left box is for entering answers, and the right box seems to provide options like checking or resetting the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffed13db8-c4fc-4284-8919-d62233846506%2Feea73090-8352-4265-a6fe-ad14fe6ab346%2Fq6wiz6i_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem, we have a piecewise defined function \( f(x) \):
\[
f(x) =
\begin{cases}
- \frac{1}{4}x - 2 & \text{if } x \neq 2 \\
-1 & \text{if } x = 2
\end{cases}
\]
We need to find the values of the function at specific points: \( f(-2) \), \( f(2) \), and \( f(4) \).
### Calculations:
1. **\( f(-2) \):**
Since \(-2 \neq 2\), use the first case:
\[
f(-2) = -\frac{1}{4}(-2) - 2 = \frac{1}{2} - 2 = -\frac{3}{2}
\]
2. **\( f(2) \):**
Since \(x = 2\), use the second case:
\[
f(2) = -1
\]
3. **\( f(4) \):**
Since \(4 \neq 2\), use the first case:
\[
f(4) = -\frac{1}{4}(4) - 2 = -1 - 2 = -3
\]
### Final Values:
- \( f(-2) = -\frac{3}{2} \)
- \( f(2) = -1 \)
- \( f(4) = -3 \)
The graph or diagrams do not represent any visual content specific to the function but provide interface elements for inputting answers in an educational tool. The left box is for entering answers, and the right box seems to provide options like checking or resetting the answer.
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