Textbook Question
Use the vertical line test to identify graphs in which y is a function of x.
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 13
Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, −√3) and (√5, 0)
Verified step by step guidance1
Identify the coordinates of the two points: Point 1 is \((0, -\sqrt{3})\) and Point 2 is \((\sqrt{5}, 0)\).
Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substitute the given coordinates into the distance formula: \(d = \sqrt{(\sqrt{5} - 0)^2 + (0 - (-\sqrt{3}))^2}\).
Simplify inside the square root: calculate \((\sqrt{5})^2\) and \((\sqrt{3})^2\), then add the results.
Express the distance in simplified radical form and then approximate the decimal value rounded to two decimal places.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distance Formula
The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √((x2 - x1)² + (y2 - y1)²). This formula helps find the straight-line distance between points (x1, y1) and (x2, y2).
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Simplified Radical Form
Simplified radical form means expressing square roots in their simplest form by factoring out perfect squares. For example, √50 can be simplified to 5√2. This form is preferred before rounding to maintain exactness and clarity in answers.
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Rounding to Decimal Places
Rounding involves approximating a number to a specified number of decimal places for simplicity. In this problem, answers are rounded to two decimal places, which means keeping two digits after the decimal point and adjusting the last digit based on the next digit's value.
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Related Practice
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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) = 2x