Domanda del libro di testo
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 27a
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x3
Guida verificata passo dopo passo1
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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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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5:26
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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4:56Function 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.
Video consigliato:
4:26Evaluating Composed Functions
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