Textbook Question
Find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)
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 46
Give the slope and y-intercept of each line whose equation is given. Then graph the linear function. y = -2x/5+6
Verified step by step guidance1
Identify the given linear equation: \(y = -\frac{2x}{5} + 6\).
Rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Here, the equation is already in this form with \(m = -\frac{2}{5}\) and \(b = 6\).
Determine the slope \(m = -\frac{2}{5}\), which means the line falls 2 units vertically for every 5 units it moves horizontally to the right.
Identify the y-intercept \(b = 6\), which is the point where the line crosses the y-axis, at \((0, 6)\).
To graph the line, start by plotting the y-intercept \((0, 6)\) on the coordinate plane, then use the slope to find another point by moving 5 units to the right and 2 units down, and draw the line through these points.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Slope of a Linear Function
The slope represents the rate of change of the function and indicates how steep the line is. It is the coefficient of x in the equation y = mx + b, where m is the slope. A negative slope means the line decreases as x increases.
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Linear Inequalities
Y-Intercept of a Linear Function
The y-intercept is the point where the line crosses the y-axis, given by the constant term b in y = mx + b. It shows the value of y when x is zero and helps in graphing the line accurately.
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Graphing Linear Functions
Graphing involves plotting the y-intercept on the coordinate plane and using the slope to find other points by rising and running from the intercept. Connecting these points forms the line representing the function.
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Related Practice
Textbook Question
Solve: 2x2/3 - 5x1/3 -3 = 0.
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Textbook Question
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. y = (2/5)x - 1
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Textbook Question
In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x)= |x|, g(x) = |x| +1
Textbook Question
Find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x)= = 9x/(x - 4), g(x) = 7/(x+8)
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Textbook Question
Find f/g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)