Mathematics, 21.02.2021 01:20 robert7248

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.

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Answer from: saneayahsimmons

$\displaystyle -1$

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: $\displaystyle \frac{f(b) - f(a)}{b - a}$

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]: $\displaystyle \frac{f(3) - f(-7)}{3 - -7}$ [Average Rate of Change] Substitute in function: $\displaystyle \frac{3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6]}{3 - -7}$ [Average Rate of Change] Simplify: $\displaystyle \frac{3^2 + 3(3) - 6 - [(-7)^2 + 3(-7) - 6]}{3 + 7}$ [Average Rate of Change] Evaluate exponents: $\displaystyle \frac{9 + 3(3) - 6 - [49 + 3(-7) - 6]}{3 + 7}$ [Average Rate of Change] Multiply: $\displaystyle \frac{9 + 9 - 6 - [49 - 21 - 6]}{3 + 7}$ [Average Rate of Change] [Brackets] Subtract: $\displaystyle \frac{9 + 9 - 6 - [28 - 6]}{3 + 7}$ [Average Rate of Change] [Brackets] Subtract: $\displaystyle \frac{9 + 9 - 6 - 22}{3 + 7}$ [Average Rate of Change] Add: $\displaystyle \frac{18 - 6 - 22}{3 + 7}$ [Average Rate of Change] Subtract: $\displaystyle \frac{12 - 22}{3 + 7}$ [Average Rate of Change] Subtract: $\displaystyle \frac{-10}{3 + 7}$ [Average Rate of Change] Add: $\displaystyle \frac{-10}{10}$ [Average Rate of Change] Divide: $\displaystyle -1$

Answer from: Quest

8/k

step-by-step explanation:

Answer from: Quest

idk

step-by-step explanation:

payback

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Given the function h(x)=x^2+3x-6h(x)=x 2
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