Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:20 minutes

Problem 3

Textbook Question

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

Verified step by step guidance

Identify the general form of a linear equation, which is y = mx + b, where x is the independent variable and y is the dependent variable.

In the given equation y = 4x - 6, compare it with the general form to identify the variables.

Recognize that the independent variable is the one that you can choose freely, which is x in this equation.

Understand that the dependent variable is the one that depends on the value of the independent variable, which is y in this equation.

Fill in the blanks: 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 of a function, often represented by 'x' in equations. It is the variable that is manipulated or changed to observe its effect on the dependent variable. In the equation y = 4x - 6, 'x' is the independent variable, as its values determine the corresponding outputs of the function.

Dependent Variable

The dependent variable is the output of a function, typically represented by 'y'. It depends on the value of the independent variable, meaning its value changes in response to the independent variable's changes. In the equation y = 4x - 6, 'y' is the dependent variable, as it is calculated based on the value of 'x'.

Function Definition

A function is a relation that assigns exactly one output for each input from its domain. In mathematical terms, a function can be expressed as an equation, where the independent variable is used to compute the dependent variable. The equation y = 4x - 6 is a linear function, illustrating how changes in 'x' directly affect 'y'.