Textbook Question
For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
Ch. 2 - Graphs and Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 3, Problem 23
Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. vertical, through (-6, 4)
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Identify the type of line described: a vertical line. Vertical lines have an undefined slope and are represented by equations of the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.
Since the line passes through the point \((-6, 4)\), the x-coordinate for all points on this vertical line is \(-6\).
Write the equation of the vertical line using the x-coordinate from the given point: \(x = -6\).
Confirm that this equation is in standard form. For vertical lines, the standard form is typically written as \(x = a\), which is already the case here.
No further simplification is needed, and the equation \(x = -6\) fully describes the vertical line through \((-6, 4)\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equation of a Vertical Line
A vertical line has an undefined slope and is represented by an equation of the form x = a, where a is the x-coordinate of every point on the line. For example, a vertical line through (-6, 4) is x = -6, meaning all points have x = -6 regardless of y.
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05:39
Standard Form of Line Equations
Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0. Vertical lines can be written in this form by setting B = 0, such as x = -6 becoming 1x + 0y = -6.
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05:39Standard Form of Line Equations
Slope-Intercept Form of a Linear Equation
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Vertical lines cannot be expressed in this form because their slope is undefined, so only non-vertical lines can be written as y = mx + b.
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Related Practice
Textbook Question
For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
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Textbook Question
For each graph, determine whether y is a function of x. Give the domain and range of each relation.
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Textbook Question
For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.
ƒ(x)=√(4x-1), g(x)=1/x
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Textbook Question
Determine whether the three points are the vertices of a right triangle. (-6,-4),(0,-2),(-10,8)
Textbook Question
Graph each piecewise-defined function.
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