Textbook Question
Find the domain of each function. h(x) = √(x −2)+ √(x +3)
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
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 25
Find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)
Verified step by step guidance1
Recall that the midpoint \( M \) of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ M = \left( \frac{ x_1 + x_2 }{ 2 }, \frac{ y_1 + y_2 }{ 2 } \right) \]
Identify the coordinates of the given endpoints:
\( x_1 = -\frac{7}{2}, \quad y_1 = \frac{3}{2} \)
\( x_2 = -\frac{5}{2}, \quad y_2 = -\frac{11}{2} \)
Substitute the values of \( x_1 \) and \( x_2 \) into the midpoint formula for the x-coordinate:
\[ x_{mid} = \frac{ -\frac{7}{2} + \left(-\frac{5}{2}\right) }{ 2 } \]
Substitute the values of \( y_1 \) and \( y_2 \) into the midpoint formula for the y-coordinate:
\[ y_{mid} = \frac{ \frac{3}{2} + \left(-\frac{11}{2}\right) }{ 2 } \]
Simplify both expressions to find the coordinates of the midpoint \( M = (x_{mid}, y_{mid}) \).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Midpoint Formula
The midpoint formula calculates the point exactly halfway between two given points in the coordinate plane. It is found by averaging the x-coordinates and the y-coordinates separately: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2). This formula helps locate the center of a line segment.
Recommended video:
06:36
Solving Quadratic Equations Using The Quadratic Formula
Coordinate Plane
The coordinate plane is a two-dimensional surface defined by a horizontal x-axis and a vertical y-axis. Points are represented as ordered pairs (x, y), where x indicates horizontal position and y indicates vertical position. Understanding this system is essential for plotting points and calculating distances or midpoints.
Recommended video:
Guided course
05:10Graphs & the Rectangular Coordinate System
Fraction Arithmetic
Working with fractions involves operations like addition, subtraction, and division. When finding midpoints with fractional coordinates, it is important to correctly add fractions and divide by 2, often requiring finding common denominators. Accurate fraction manipulation ensures precise midpoint calculation.
Recommended video:
Guided course
5:17Arithmetic Sequences - General Formula
Related Practice
Textbook Question
In Exercises 11–26, determine whether each equation defines y as a function of x. |x| − y = 2
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) = (x +4)/(x-2)
Textbook Question
Use the graph of y = f(x) to graph each function g.
g(x) = f(-x)+1
1
views
Textbook Question
Use the graph of y = f(x) to graph each function g. g(x) = -f(x)+1
5
views
Textbook Question
Determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.