https://file.aiquickdraw.com/mathbot/file/1726558528615ps4qiwc1.jpg

From the image provided, it appears to contain several mathematical tasks written down. Here's a breakdown of the relevant parts:

1. **Task (1)** involves plotting the graph of a trigonometric function:  
   \[
   y = 2 \cdot \cos(x - 30^\circ) + 1
   \]
   for the interval \(90^\circ \leq x \leq 270^\circ\).

2. **Task (2)** appears to ask for another graph to be plotted. It's labeled but partially obscured, and I would need a bit of clarification on this part.

3. **Task (3)** seems to involve a function:
   \[
   f(x) = 2.3
   \]
   and it is followed by solving the quadratic expression:  
   \[
   2x^2 - x + 3
   \]
   where the rest might involve solving or graphing this quadratic equation.

4. **Task (4)** introduces a rational function:
   \[
   f(x) = \frac{x - 4}{x + 2}
   \]
   which might involve analyzing its domain, asymptotes, or graphing it.

To provide a complete solution, I would need more context on tasks 2 and 4, as they are slightly obscured in the image. Could you clarify those parts? Or should I proceed with solving tasks 1, 3, and 4 based on the current information?

Feel free to ask for details, and here are 5 related questions to deepen the discussion:

1. Do you need a detailed explanation for plotting the trigonometric function in Task (1)?
2. Would you like me to solve the quadratic equation in Task (3)?
3. Is there any particular aspect of the rational function in Task (4) that you would like to focus on?
4. Should I check for the domain and range of the functions?
5. Would you like a step-by-step breakdown of how to solve or graph these functions?

**Tip:** When plotting a trigonometric function like \( y = A \cos(B(x - C)) + D \), it’s helpful to identify the amplitude \(A\), period \( \frac{360^\circ}{B} \), phase shift \(C\), and vertical shift \(D\) for a clearer understanding of how the graph behaves.

The original question involves graphing trigonometric functions, solving quadratic equations, and working with rational functions.

Learn how to graph the trigonometric function y = 2 * cos(x - 30°) + 1 for the interval 90° ≤ x ≤ 270°, solve the quadratic equation 2x² - x + 3, and analyze the rational function (x - 4) / (x + 2). This solution provides a detailed explanation for students in Grades 9-12.

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