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.

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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 

**Educational Website Content: Continuity and Transformations in Functions**

---

**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.
Transcribed Image Text:**Educational Website Content: Continuity and Transformations in Functions** --- **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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