The functions f (x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3 < x < 9 goes from least to greatest.
The functions f (x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3 < x < 9 goes from least to greatest.
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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![The educational content focuses on comparing the average rates of change of three functions, \( f(x) \), \( g(x) \), and \( h(x) \), over the interval \( 3 \leq x \leq 9 \).
1. **Graph of \( f(x) \):**
- The graph is a plot on a Cartesian plane with \( x \) ranging from \(-10\) to \(10\) and \( y \) values from \(-100\) to \(100\).
- The curve is a smooth polynomial that appears to have turning points and passes through specific coordinates marked on the plot.
2. **Table for \( g(x) \):**
- A table lists values of \( g(x) \) for different \( x \):
\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
3 & 35 \\
6 & 14 \\
9 & 11 \\
12 & 26 \\
\hline
\end{array}
\]
3. **Equation for \( h(x) \):**
- The function \( h(x) \) is defined by the quadratic equation:
\[
h(x) = x^2 - 5x - 2
\]
To solve the problem, one would calculate the average rate of change for each function over the specified interval and order them from least to greatest. The average rate of change is typically computed using the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a \) and \( b \) are the interval endpoints, here \( 3 \) and \( 9 \). Once calculated for each function, the rates are compared to determine the correct ordering.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd46f87c7-9f35-413e-a6ca-eb5fe759983b%2F826205a3-9d02-41d8-bc12-a65b25b2608e%2F3jmquib_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The educational content focuses on comparing the average rates of change of three functions, \( f(x) \), \( g(x) \), and \( h(x) \), over the interval \( 3 \leq x \leq 9 \).
1. **Graph of \( f(x) \):**
- The graph is a plot on a Cartesian plane with \( x \) ranging from \(-10\) to \(10\) and \( y \) values from \(-100\) to \(100\).
- The curve is a smooth polynomial that appears to have turning points and passes through specific coordinates marked on the plot.
2. **Table for \( g(x) \):**
- A table lists values of \( g(x) \) for different \( x \):
\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
3 & 35 \\
6 & 14 \\
9 & 11 \\
12 & 26 \\
\hline
\end{array}
\]
3. **Equation for \( h(x) \):**
- The function \( h(x) \) is defined by the quadratic equation:
\[
h(x) = x^2 - 5x - 2
\]
To solve the problem, one would calculate the average rate of change for each function over the specified interval and order them from least to greatest. The average rate of change is typically computed using the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a \) and \( b \) are the interval endpoints, here \( 3 \) and \( 9 \). Once calculated for each function, the rates are compared to determine the correct ordering.
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