Question

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Answer 1

`\displaystyle -1`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Interval Notation
• Function Notation
• Average Rate of Change:
  `\displaystyle (f(b) - f(a))/(b - a)`

Explanation:

Step 1: Define

h(x) = x² + 3x - 6

[-7, 3] → a = -7, b = 3

Step 2: Find Average

1. Substitute in variables [Average Rate of Change]:
   `\displaystyle (f(3) - f(-7))/(3 - -7)`
2. [Average Rate of Change] Substitute in function:
   `\displaystyle (3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6])/(3 - -7)`
3. [Average Rate of Change] Simplify:
   `\displaystyle (3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6])/(3 + 7)`

1. [Average Rate of Change] Evaluate exponents:
   `\displaystyle (9 + 3(3) - 6 - [49 + 3(-7) - 6])/(3 + 7)`
2. [Average Rate of Change] Multiply:
   `\displaystyle (9 + 9 - 6 - [49 - 21 - 6])/(3 + 7)`
3. [Average Rate of Change] [Brackets] Subtract:
   `\displaystyle (9 + 9 - 6 - [28 - 6])/(3 + 7)`
4. [Average Rate of Change] [Brackets] Subtract:
   `\displaystyle (9 + 9 - 6 - 22)/(3 + 7)`
5. [Average Rate of Change] Add:
   `\displaystyle (18 - 6 - 22)/(3 + 7)`
6. [Average Rate of Change] Subtract:
   `\displaystyle (12 - 22)/(3 + 7)`
7. [Average Rate of Change] Subtract:
   `\displaystyle (-10)/(3 + 7)`
8. [Average Rate of Change] Add:
   `\displaystyle (-10)/(10)`
9. [Average Rate of Change] Divide:
   `\displaystyle -1`