Textbook Question
Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).
h(x) = |2x-5|
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 79
Find the value of y if the line through the two given points is to have the indicated slope. (3, y) and (1, 4), m = −3
Verified step by step guidance1
Recall the formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
Identify the given points and slope:
Point 1: \((3, y)\), Point 2: \((1, 4)\), and slope \(m = -3\).
Substitute the known values into the slope formula:
\[-3 = \frac{4 - y}{1 - 3}\]
Simplify the denominator:
\[-3 = \frac{4 - y}{-2}\]
Solve the equation for \(y\) by multiplying both sides by \(-2\) and then isolating \(y\).
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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 of a line measures its steepness and is calculated as the ratio of the change in y-values to the change in x-values between two points. It is given by m = (y2 - y1) / (x2 - x1). Understanding slope is essential to relate the points and the given slope.
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06:49
The Slope of a Line
Using Coordinates to Find Unknown Values
When one coordinate is unknown, you can use the slope formula and the known slope to set up an equation. By substituting the known values and solving for the unknown coordinate, you find the missing value that satisfies the slope condition.
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05:10Graphs & the Rectangular Coordinate System
Solving Linear Equations
After substituting values into the slope formula, you get a linear equation in terms of the unknown variable. Solving this equation involves basic algebraic manipulation such as addition, subtraction, multiplication, or division to isolate and find the unknown.
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04:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; and e. the missing function values, indicated by question marks, below each graph.
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Textbook Question
Find the domain of each function.
Textbook Question
Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = 2√(x+1)-1
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Textbook Question
In Exercises 77–92, use the graph to determine a. the function's range; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.
Textbook Question
Use the graph to determine a.the x-intercepts, if any; b. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.