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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 3
Chapter 3, Problem 3

Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

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Identify the independent variable as the variable that you can choose freely or input into the function. In the equation \(y = 4x - 6\), this is the variable \(x\).
Identify the dependent variable as the variable that depends on the independent variable's value. In the equation \(y = 4x - 6\), this is the variable \(y\) because its value changes based on \(x\).
Therefore, the independent variable is \(x\) and the dependent variable is \(y\).
Understand that in functions, the independent variable is often called the input, and the dependent variable is the output.
So, the completed sentence is: The equation \(y = 4x - 6\) defines a function with independent variable \(x\) and dependent variable \(y\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Independent Variable

The independent variable is the input or the variable you can freely choose in a function. In the equation y = 4x - 6, x is the independent variable because its values determine the output values of y.
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Dependent Variable

The dependent variable depends on the independent variable and represents the output of the function. In y = 4x - 6, y is the dependent variable because its value changes based on the value chosen for x.
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Function Definition

A function relates each input to exactly one output. The equation y = 4x - 6 defines a function where each x-value corresponds to one y-value, illustrating the relationship between independent and dependent variables.
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Related Practice
Textbook Question

Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.

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Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2

(ƒ−g)(2)(ƒ-g)(2)

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Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2

(ƒg)(2)

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Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x3? What is its range?

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Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. A(-6, 3), B(-6,8)

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Textbook Question

Find the distance between each pair of points, and give the coordinates of the midpoint of the line segment joining them. M(-8, 2), N(3, -7)