Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = f(x/2)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 13
Find the average rate of change of the function from x1 to x2. f(x) = 3x from x1 = 0 to x2 = 5
Verified step by step guidance1
Identify the function given: \(f(x) = 3x\).
Note the interval over which to find the average rate of change: from \(x_1 = 0\) to \(x_2 = 5\).
Recall the formula for the average rate of change of a function \(f(x)\) over the interval \([x_1, x_2]\):
\[\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}\]
Calculate \(f(x_1)\) and \(f(x_2)\) by substituting the values into the function:
\[f(0) = 3 \times 0\]
\[f(5) = 3 \times 5\]
Substitute these values into the average rate of change formula and simplify the expression (without calculating the final numeric value).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Average Rate of Change
The average rate of change of a function over an interval measures how much the function's output changes per unit change in input. It is calculated as the difference in function values divided by the difference in input values, similar to the slope of a secant line between two points on the graph.
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Change of Base Property
Evaluating Functions at Given Points
To find the average rate of change, you must first evaluate the function at the specified input values. This involves substituting the given x-values into the function expression to find the corresponding y-values or outputs.
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4:26Evaluating Composed Functions
Linear Functions and Their Properties
A linear function like f(x) = 3x has a constant rate of change, meaning the average rate of change between any two points is the same as the slope of the line. Understanding this helps simplify calculations and interpret results quickly.
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5:36Change of Base Property
Related Practice
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