Question

What is the average rate of change of the function g(x) = 4x from x = 1 to x = 5?

Answer 1

`\displaystyle 4`

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

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

Explanation:

Step 1: Define

g(x) = 4x

Interval [1, 5]

Step 2: Find Change

1. Substitute in function and points [Average Rate of Change]:
   `\displaystyle \displaystyle (4(5) - 4(1))/(5 - 1)`
2. [Fraction] Multiply:
   `\displaystyle \displaystyle (20 - 4)/(5 - 1)`
3. [Fraction] Subtract:
   `\displaystyle \displaystyle (16)/(4)`
4. [Fraction] Divide:
   `\displaystyle 4`