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Use the graph of y = f(x) to graph each function g. g(x) = f(x + 1) − 2
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 23
Find the midpoint of each line segment with the given endpoints. (-3, -4) and (6, −8)
Guida verificata passo dopo passo1
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: \( (x_1, y_1) = (-3, -4) \) and \( (x_2, y_2) = (6, -8) \).
Substitute the values into the midpoint formula:
\[ M = \left( \frac{ -3 + 6 }{ 2 }, \frac{ -4 + (-8) }{ 2 } \right) \]
Simplify the expressions inside the parentheses separately:
\[ \frac{ -3 + 6 }{ 2 } = \frac{3}{2} \quad \text{and} \quad \frac{ -4 + (-8) }{ 2 } = \frac{ -12 }{ 2 } \]
Write the midpoint as the ordered pair using the simplified values:
\[ M = \left( \frac{3}{2}, -6 \right) \]
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Coordinate Plane and Points
The coordinate plane is a two-dimensional system where each point is defined by an ordered pair (x, y). Understanding how to plot and interpret points is essential for visualizing line segments and their properties.
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05:10
Graphs & the Rectangular Coordinate System
Line Segment
A line segment is the part of a line bounded by two endpoints. Knowing the endpoints allows us to analyze properties like length and midpoint, which are fundamental in geometry and algebra.
Video consigliato:
06:49The Slope of a Line
Midpoint Formula
The midpoint formula calculates the point exactly halfway between two endpoints. It is given by ((x1 + x2)/2, (y1 + y2)/2), averaging the x-coordinates and y-coordinates separately to find the midpoint.
Video consigliato:
06:36Solving Quadratic Equations Using The Quadratic Formula
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