Given the function h(x)=x^2+3x-6h(x)=x 2
+3x−6, determine the average rate of change of the function over the interval -7\le x \le 3−7≤x≤3.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Interval NotationFunction NotationAverage Rate of Change:

Step-by-step explanation:

Step 1: Define

h(x) = x² + 3x - 6

[-7, 3] → a = -7, b = 3

Step 2: Find Average

Substitute in variables [Average Rate of Change]:                                      [Average Rate of Change] Substitute in function:                                       [Average Rate of Change] Simplify:                                                               [Average Rate of Change] Evaluate exponents:                                           [Average Rate of Change] Multiply:                                                              [Average Rate of Change] [Brackets] Subtract:                                            [Average Rate of Change] [Brackets] Subtract:                                            [Average Rate of Change] Add:                                                                     [Average Rate of Change] Subtract:                                                                [Average Rate of Change] Subtract:                                                               [Average Rate of Change] Add:                                                                     [Average Rate of Change] Divide:                                                                

Ithink it’s d as the answer.