Skip to main content
Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblem 100
Chapter 4, Problem 100

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

Verified step by step guidance
1
Identify the function and the interval: The function is f(x)=x, and the interval is from x1 = 4 to x2 = 9.
Recall the formula for the average rate of change of a function f over an interval [x_1, x_2]: \(\frac{f(x_2) - f(x_1)}{x_2 - x_1}\).
Calculate the function values at the endpoints: find f(4) = \(\sqrt{4}\) and f(9) = \(\sqrt{9}\).
Substitute the values into the average rate of change formula: \(\frac{f(9) - f(4)}{9 - 4}\).
Simplify the expression by evaluating the square roots and performing the subtraction and division to find the average rate of change.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
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 on the graph.
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 nonlinear function that increases at a decreasing rate, meaning its graph is a curve that flattens as x increases.
Recommended video:
02:20
Imaginary Roots with the Square Root Property

Evaluating Function Values

To find the average rate of change, you must evaluate the function at the given points x1 and x2. This involves substituting the x-values into the function to find f(x1) and f(x2), which are then used to compute the difference quotient.
Recommended video:
4:26
Evaluating Composed Functions
Related Practice
Textbook Question

Exercises 107–109 will help you prepare for the material covered in the next section. Factor: x3+3x2−x−3

871
views
Textbook Question

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-1) The graph passes through the point (-2,-3).

1613
views
Textbook Question

Exercises 107–109 will help you prepare for the material covered in the next section. Determine whether f(x)=x4−2x2+1 is even, odd, or neither. Describe the symmetry, if any, for the graph of f.

851
views
Textbook Question

Solve: x4−6x3+4x2+15x+4=0x^4−6x^3+4x^2+15x+4=0.

654
views
Textbook Question

Use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x)=(3x−7)/(x−2)

638
views
Textbook Question

In Exercises 97–98, write the equation of each parabola in vertex form. Vertex: (-3,-4) The graph passes through the point (1,4).

1135
views