https://file.aiquickdraw.com/mathbot/file/1726091022274bhv7oyah.jpg

Let's solve problems 2 and 14 from the image:

### Problem 2:
**Given:**
\[ f(y) = y^2 + y - 6 \]
Find:
1. \( f(2) \)
2. \( f(-1) \)
3. \( f(0) \)

**Solution:**
1. For \( f(2) \):
   \[
   f(2) = 2^2 + 2 - 6 = 4 + 2 - 6 = 0
   \]
2. For \( f(-1) \):
   \[
   f(-1) = (-1)^2 + (-1) - 6 = 1 - 1 - 6 = -6
   \]
3. For \( f(0) \):
   \[
   f(0) = 0^2 + 0 - 6 = -6
   \]

### Problem 14:
**Given interval:** \((-1.5, 4.5)\)

**Task:** Write the inequality representation of the interval.

**Solution:**
The interval \((-1.5, 4.5)\) can be represented as an inequality:
\[
-1.5 < x < 4.5
\]

Would you like further explanations or have any questions?

### Follow-Up Questions:
1. How do you solve for \(f(x)\) when given different values of \(x\)?
2. How do you convert intervals into inequalities?
3. What are open and closed intervals in interval notation?
4. How would the solution change if \(x\) were included in the endpoints for Problem 14?
5. Can you explain why \(f(0)\) and \(f(-1)\) have the same value in Problem 2?

**Tip:** Always substitute the given values correctly in functions, and remember to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Learn how to solve the function f(x) = x^2 + x - 6 for various values of x and convert the interval (-1.5, 4.5) into inequality form. A clear explanation is provided for students in grades 8-10.

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