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Multiply or divide, as indicated. See Example 3. ((2k + 8) / 6) ÷ ((3k + 12) / 2)
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 35
Determine whether each relation defines y as a function of x. Give the domain and range. See Example 5. y = 2x - 5
Guida verificata passo dopo passo1
Identify the given relation: \(y = 2x - 5\). This is an equation expressing \(y\) explicitly in terms of \(x\).
Determine if \(y\) is a function of \(x\): Since for every value of \(x\) there is exactly one corresponding value of \(y\) (because the equation is linear and passes the vertical line test), \(y\) is indeed a function of \(x\).
Find the domain: Since there are no restrictions on \(x\) in the equation \(y = 2x - 5\), the domain is all real numbers, which can be written as \((-\infty, \infty)\).
Find the range: Because \(y\) is a linear function with no restrictions, it can take any real value as \(x\) varies over all real numbers. Therefore, the range is also \((-\infty, \infty)\).
Summarize: The relation defines \(y\) as a function of \(x\) with domain \((-\infty, \infty)\) and range \((-\infty, \infty)\).
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Definition of a Function
A function is a relation where each input (x-value) corresponds to exactly one output (y-value). To determine if y is a function of x, check if for every x there is only one y. The given equation y = 2x - 5 is a linear function, so it passes this test.
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Percorso guidato
5:57
Graphs of Common Functions
Domain of a Function
The domain is the set of all possible input values (x-values) for which the function is defined. For the linear function y = 2x - 5, the domain is all real numbers because any real x can be substituted without restriction.
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Percorso guidato
3:43Finding the Domain of an Equation
Range of a Function
The range is the set of all possible output values (y-values) that the function can produce. Since y = 2x - 5 is linear with no restrictions, its range is also all real numbers, as y can take any real value depending on x.
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Percorso guidato
4:22Domain and Range of Function Transformations
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