I need help with this I sent a picture thank you # Educational Content: Average Rate of Change## Problem StatementIn this exercise, you are tasked with analyzing two functions, \( f(x) \) and \( g(x) \), to determine which function has the greater average rate of change over a specified interval. Below is the detailed explanation and description of the functions involved.### Functions1. **Function \( f(x) \):** \[ f(x) = x^2 + 3x \]2. **Function \( g(x) \):** values are given in a table:| \( x \) | \( g(x) \) ||---------|----------|| 0 | -3 || 2 | 4 || 3 | 11 || 5 | 24 || 6 | 36 || 8 | 43 || 10 | 46 |### TaskYou are asked to calculate the average rate of change for both functions over the interval \([2, 6]\) and determine which has the greater rate of change. Be sure to show your reasoning and calculations, as answers without supporting work will receive partial credit only.### How to Calculate Average Rate of ChangeThe average rate of change of a function over an interval \([a, b]\) is given by the formula:\[\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}\]Apply this formula to both functions over the specified interval:#### For \( f(x) \):- Calculate \( f(6) \) and \( f(2) \)- Substitute into the formula#### For \( g(x) \):- Use the table values \( g(6) \) and \( g(2) \)- Substitute into the same formula### ConclusionDetermine which function, \( f(x) \) or \( g(x) \), has the larger average rate of change based on your calculations. Provide a clear and concise explanation to support your findings. **Part III Questions:**Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps and explain your reasoning. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.**12. Two functions, \( f(x) \) and \( g(x) \), are given below. Determine which of these functions has the greater average rate of change over the interval \( 2 \leq x \leq 6 \). Support your final answer.**- \( f(x) = x^2 + 3x \)A table for \( g(x) \) is provided as follows:\[\begin{array}{|c|c|}\hlinex & g(x) \\\hline-3 & 2 \\0 & 3 \\2 & 5 \\3 & 6 \\5 & 8 \\6 & 10 \\8 & 11 \\10 & 12 \\\hline\end{array}\]**Explanation of the Diagram:**The diagram likely includes two parts: a depiction of a function and a note indicating “function over” with a rough sketch possibly highlighting a parabolic curve with annotations crossing out and correcting a drawn feature.

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Answered: Il. ILMOUTS 12. Two functions, f (x)…

Il. ILMOUTS 12. Two functions, f (x) and g(x), are given below. Determine which of these functions has the rate of change over the interval 2 < x <6. Support your final answer. f (x)= x² + 3x

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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