Textbook Question
Which graphs in Exercises 29–34 represent functions that have inverse functions?
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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 30
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−2, −4) and (1, −1)
Verified step by step guidance1
Identify the two given points: \((-2, -4)\) and \((1, -1)\).
Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1) = (-2, -4)\) and \((x_2, y_2) = (1, -1)\).
Use the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), substituting \(m\) and one of the points (either \((-2, -4)\) or \((1, -1)\)).
Simplify the point-slope form equation if needed, but keep it in the form \(y - y_1 = m(x - x_1)\) for the point-slope form answer.
Convert the point-slope form to slope-intercept form \(y = mx + b\) by solving for \(y\) and simplifying the expression.
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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 change in y-values divided by the change in x-values between two points. For points (x₁, y₁) and (x₂, y₂), slope m = (y₂ - y₁) / (x₂ - x₁). It is essential for writing the equation of a line.
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The Slope of a Line
Point-Slope Form of a Line
Point-slope form expresses a line's equation using a known point (x₁, y₁) and the slope m: y - y₁ = m(x - x₁). This form is useful when you know a point on the line and its slope, allowing you to write the equation directly.
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05:46Point-Slope Form
Slope-Intercept Form of a Line
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form clearly shows the line's slope and where it crosses the y-axis.
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Related Practice
Textbook Question
In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (√50, −6) and (√2, 6)
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Textbook Question
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 b. g(x+2)
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Textbook Question
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.g(x) = x² + 2x + 3 a. g(-1)
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Textbook Question
Evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 c. g(-x)
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Textbook Question
Evaluate each function at the given values of the independent variable and simplify. g(x) = x² - 10x - 3 a. g(-1)
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