Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 17
Chapter 3, Problem 17

Find the average rate of change of the function from x1 to x2. f(x) = √x from x1 = 4 to x2 = 9

Verified step by step guidance
1
Identify the function given: \(f(x) = \sqrt{x}\), and the interval endpoints \(x_1 = 4\) and \(x_2 = 9\).
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 the function values at the endpoints: \(f(x_1) = f(4) = \sqrt{4}\) and \(f(x_2) = f(9) = \sqrt{9}\).
Substitute these values into the average rate of change formula: \(\frac{\sqrt{9} - \sqrt{4}}{9 - 4}\).
Simplify the numerator and denominator separately, then divide to find the average rate of change over the interval.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

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 between two points 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 connecting the two points.
Recommended video:
5:36
Change of Base Property

Square Root Function

The square root function, denoted as f(x) = √x, outputs the non-negative number whose square is x. It is defined for x ≥ 0 and is a common example of a radical function, which often requires careful evaluation when calculating function values at specific points.
Recommended video:
02:20
Imaginary Roots with the Square Root Property

Evaluating Functions at Given Points

To find the average rate of change, you must correctly evaluate the function at the specified input values. This involves substituting the input values into the function and simplifying, ensuring accurate calculation of the function's outputs at those points.
Recommended video:
4:26
Evaluating Composed Functions
Related Practice
Textbook Question

The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ-1 (x)) = = x and ƒ-1 (f(x)) = x. f(x) = x³ +2

637
views
Textbook Question

In Exercises 11–26, determine whether each equation defines y as a function of x. x = y²

82
views
Textbook Question

Use the graph of y = f(x) to graph each function g.

g(x) = f(x) - 1

925
views
Textbook Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = -5, passing through (-4, -2)

90
views
Textbook Question

In Exercises 1-16, use the graph of y = f(x) to graph each function g.

g(x) = -f(2x) - 1

753
views
Textbook Question

Find the domain of each function. f(x) = 1/[4/(x - 1) - 2]

857
views