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The document you uploaded contains a set of exercises from a *Calculus I* reinforcement activity. Here's a summary of the problems mentioned:

1. **Linear Function**: Find the domain and range of $ f(x) = 2x + 3 $.
2. **Quadratic Function**: Graph $ g(x) = x^2 - 4x + 3 $ and determine its domain and range.
3. **Contextualized Problem**: Calculate the total cost for renting a bicycle using the function $ c(t) = 10t + 20 $ after 4 hours.
4. **Trigonometric Function**: Graph $ y = 2\sin(x) $ and determine its amplitude, period, and vertical shift.
5. **Trig Equation**: Solve $ 3\cos(x) = 2 $ for $ x $ in the interval $ [0, 2\pi] $.
6. **Contextualized Trig Problem**: Find the maximum distance between an observer and a boat using $ y(t) = 50 + 30\sin\left(\frac{\pi t}{6}\right) $.
7. **Inverse Function**: Verify and find the inverse of $ f(x) = 3x - 2 $.
8. **Inverse of Rational Function**: Find the inverse of $ g(x) = \frac{4}{x} $.
9. **Contextualized Inverse Problem**: Determine how many T-shirts a customer should buy to spend $100 using the function $ C(p) = 20p $.

If you need solutions to any of these problems or further explanation, let me know.

Would you like detailed solutions to any of the exercises?

Here are five related questions that may help:
1. How do you find the domain and range of a function?
2. What are the critical points of a quadratic function and how do they help in graphing?
3. What is the method for determining the period of a trigonometric function?
4. How can you verify if a function has an inverse?
5. What are the applications of inverse functions in real-life problems?

**Tip**: When solving trigonometric equations like $ 3\cos(x) = 2 $, always check if the result is valid within the domain of the cosine function!

The document you uploaded contains a set of exercises from a Calculus I reinforcement activity. Here's a summary of the problems mentioned:

1. Linear Function: Find the domain and range of f(x) = 2x + 3.
2. Quadratic Function: Graph g(x) = x^2 - 4x + 3 and determine its domain and range.
3. Contextualized Problem: Calculate the total cost for renting a bicycle using the function c(t) = 10t + 20 after 4 hours.
4. Trigonometric Function: Graph y = 2sin(x) and determine its amplitude, period, and vertical shift.
5. Trig Equation: Solve 3cos(x) = 2 for x in the interval [0, 2pi].
6. Contextualized Trig Problem: Find the maximum distance between an observer and a boat using y(t) = 50 + 30sin(pi t/6).
7. Inverse Function: Verify and find the inverse of f(x) = 3x - 2.
8. Inverse of Rational Function: Find the inverse of g(x) = 4/x.
9. Contextualized Inverse Problem: Determine how many T-shirts a customer should buy to spend $100 using the function C(p) = 20p.

Explore detailed solutions to Calculus I problems, including linear functions, quadratic functions, trigonometric functions, and inverse functions. Learn how to find domain, range, amplitude, and inverse functions with step-by-step guides.

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