Textbook Question
Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)
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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 3
Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-2, 1) and (2, 2)
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Identify the coordinates of the two points: \((-2, 1)\) and \((2, 2)\), where the first point is \((x_1, y_1) = (-2, 1)\) and the second point is \((x_2, y_2) = (2, 2)\).
Recall the formula for the slope \(m\) of a line passing through two points: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the coordinates into the slope formula: \(m = \frac{2 - 1}{2 - (-2)}\).
Simplify the numerator and denominator separately: numerator is \(2 - 1\), denominator is \(2 + 2\).
Determine the slope by dividing the simplified numerator by the simplified denominator, then analyze the sign of the slope to decide if the line rises (positive slope), falls (negative slope), is horizontal (slope zero), or vertical (undefined slope).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope of a Line
The slope measures the steepness of a line and is calculated as the ratio of the change in y-values to the change in x-values between two points, expressed as (y2 - y1) / (x2 - x1). It indicates how much y changes for a unit change in x.
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The Slope of a Line
Undefined Slope
A slope is undefined when the line is vertical, meaning the x-values of the two points are the same. Since division by zero is undefined, the slope formula cannot be applied, indicating a vertical line.
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Interpreting Slope Direction
The sign of the slope indicates the line's direction: a positive slope means the line rises from left to right, a negative slope means it falls, zero slope means the line is horizontal, and an undefined slope means the line is vertical.
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Related Practice
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Determine whether each relation is a function. Give the domain and range for each relation.{(1, 2), (3, 4), (5, 5)}
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