Question

Find the average rate of change of the function f(x) = -1x^2-7x-8 over the interval (1, 3).

Answer 1

Explanation:

-1x^2-7x8

-1x^2-7x+8

-1x+8-7x

+1x +1x

----- ------

X -7x

8 -7x

---- -----

+7 +7

---- -----

15 1x/x

15 1x

---- -----

1 X

X=15

Before you do the actual work you have to study your times table that way it helps you to be fast and it will help you to work good underpressure when it comes to integers.

What you do to one side you do to the other.

Answer 2

`\displaystyle -11`

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

Distributive Property

Algebra I

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

Explanation:

Step 1: Define

f(x) = -x² - 7x - 8

(1, 3) → a = 1, b = 3

Step 2: Find Average Rate

1. Substitute in variables [Average Rate of Change]:
   `\displaystyle \displaystyle (f(3) - f(1))/(3 - 1)`
2. [Change] Substitute in function:
   `\displaystyle \displaystyle ([-(3)^2 - 7(3) - 8] - [-(1)^2 - 7(1) - 8])/(3 - 1)`
3. [Change] [Fraction] [Brackets] Evaluate exponents:
   `\displaystyle \displaystyle ([-9 - 7(3) - 8] - [-1 - 7(1) - 8])/(3 - 1)`
4. [Change] [Fraction] [Brackets] Multiply:
   `\displaystyle \displaystyle ([-9 - 21 - 8] - [-1 - 7 - 8])/(3 - 1)`
5. [Change] [Fraction] [Brackets] Subtract:
   `\displaystyle \displaystyle ([-38] - [-16])/(2)`
6. [Change] [Fraction] [Distributive Property] Distribute negative:
   `\displaystyle \displaystyle (-38 + 16)/(2)`
7. [Change] [Fraction] Add:
   `\displaystyle \displaystyle (-22)/(2)`
8. [Change] [Fraction] Divide:
   `\displaystyle -11`