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Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = ∛(x² – 9)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 78
Give the slope and y-intercept of each line whose equation is given. Assume that B ≠ 0. Ax = By - C
Guida verificata passo dopo passo1
Start with the given equation: $Ax = By - C$.
Rearrange the equation to solve for \(y\) in terms of \(x\). Add \(C\) to both sides and then divide both sides by \(B\):
\(By = Ax + C \implies y = \frac{A}{B}x + \frac{C}{B}\).
Identify the slope \(m\) from the equation in slope-intercept form $y = mx + b$. Here, the slope is \(m = \frac{A}{B}\).
Identify the y-intercept \(b\) from the equation. The y-intercept is the constant term \(b = \frac{C}{B}\).
Summarize: The slope of the line is \(\frac{A}{B}\) and the y-intercept is \(\frac{C}{B}\).
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Slope-Intercept Form of a Line
The slope-intercept form of a line is y = mx + b, where m represents the slope and b represents the y-intercept. Converting a given equation into this form helps identify these values directly.
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02:35
Graphing Lines in Slope-Intercept Form
Rearranging Linear Equations
To find the slope and y-intercept from an equation like Ax = By - C, you must isolate y on one side. This involves algebraic manipulation such as adding, subtracting, and dividing terms to rewrite the equation in slope-intercept form.
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06:00Categorizing Linear Equations
Slope and Y-Intercept Definitions
The slope measures the steepness of a line, calculated as the ratio of vertical change to horizontal change. The y-intercept is the point where the line crosses the y-axis, found by setting x = 0 in the equation.
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03:56Slope-Intercept Form
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