1. Determine the intervals of each domain overwhich the function is continuous. +10 8 2 3 -2 F1 1 2 3 www.analyzemath.com Answer: For #2,3 Let f(x) ={x-2 if x < 3 {5- x if x2 3 2. Find f(3) 3. Find f(-5) 2.
1. Determine the intervals of each domain overwhich the function is continuous. +10 8 2 3 -2 F1 1 2 3 www.analyzemath.com Answer: For #2,3 Let f(x) ={x-2 if x < 3 {5- x if x2 3 2. Find f(3) 3. Find f(-5) 2.
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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can you please help with 1 and 2? thank you so much

Transcribed Image Text:**Educational Website Content: Continuity and Transformations in Functions**
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**1. Determine the intervals of each domain over which the function is continuous.**
The graph provided shows a piecewise function composed of segments joined between specific points. Note the open and closed circles which indicate whether endpoints are included or not.
*Graph Details:*
- The x-axis ranges from -3 to 3.
- The y-axis ranges from 0 to 10.
- The function appears continuous except for a point at \(x = 1\) where there is a break.
**Answer:** ___________________
**2. & 3. Given \(f(x) = \begin{cases}
x - 2 & \text{if } x < 3 \\
5 - x & \text{if } x \geq 3
\end{cases}**
2. **Find \(f(3)\):**
*Answer:* ___________________
3. **Find \(f(-5)\):**
*Answer:* ___________________
**4. Compare each function to \(y = |x|\). Choose the correct description for each equation.**
A) \(y = |x + 3|\)
a. A translation 3 units up.
b. A translation 3 units down.
c. A translation 3 units left.
d. A translation 3 units right.
*Answer:* ___________________
B) \(y = 2|x|\)
a. A vertical stretching by a factor of 2
b. A translation 2 units up.
c. A vertical shrinking of a factor of 2
d. A translation 2 units down.
*Answer:* ___________________
---
Please select the correct transformations for each given function and analyze the continuity of the given piecewise function accordingly.
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