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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 27a
Chapter 2, Problem 27a

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x3

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Identify the given equation: y = x^3. This is a cubic function, which means the graph will have a characteristic S-shape, passing through the origin (0, 0).
Create a table of values for the given x-values: x = -3, -2, -1, 0, 1, 2, 3. For each x-value, substitute it into the equation y = x^3 to calculate the corresponding y-value. For example, when x = -3, y = (-3)^3 = -27.
Complete the table of values by calculating y for all the given x-values. The table will look like this: x = -3, -2, -1, 0, 1, 2, 3 and corresponding y-values will be calculated as y = x^3.
Plot the points from the table of values on a coordinate plane. For example, plot (-3, -27), (-2, -8), (-1, -1), (0, 0), (1, 1), (2, 8), and (3, 27).
Draw a smooth curve through the plotted points to represent the graph of the cubic function y = x^3. Ensure the curve reflects the S-shape characteristic of cubic functions, with the graph decreasing for negative x-values, passing through the origin, and increasing for positive x-values.

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Key Concepts

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

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visualize the relationship between the input (x-values) and output (y-values). For the equation y = x^3, each x-value corresponds to a specific y-value calculated by cubing x. Understanding how to plot these points accurately is essential for interpreting the function's behavior.
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Graphs of Logarithmic Functions

Cubic Functions

Cubic functions are polynomial functions of degree three, characterized by their general form y = ax^3 + bx^2 + cx + d. The function y = x^3 is a simple cubic function where a = 1, b = 0, c = 0, and d = 0. These functions typically exhibit an S-shaped curve and can have one or two turning points, influencing their graph's shape and direction.
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Function Composition

Evaluating Functions

Evaluating functions involves substituting specific values for the variable to find corresponding outputs. In this case, substituting x = -3, -2, -1, 0, 1, 2, and 3 into the equation y = x^3 allows us to calculate the y-values. This process is crucial for generating the points needed to accurately graph the function.
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Evaluating Composed Functions
Related Practice
Textbook Question

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3

y = x3 - 1

Textbook Question

The length of a rectangular pool is 6 meters less than twice the width. If the pool's perimeter is 126 meters, what are its dimensions?

Textbook Question

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2

Textbook Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 5x + 11 < 26

Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2

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