Math Problem Statement

Graph the function. Identify three points on the graph. f left parenthesis x right parenthesis equals x cubed x=-1,0,1

Solution

The graph above shows the function f(x)=x3f(x) = x^3. The three points on the graph corresponding to x=1x = -1, x=0x = 0, and x=1x = 1 are:

  • (1,1)(-1, -1)
  • (0,0)(0, 0)
  • (1,1)(1, 1)

Would you like a more detailed explanation of the graph or the function? Here are five related questions:

  1. How does the graph of x3x^3 compare to other polynomial functions?
  2. What are the key features of cubic functions like f(x)=x3f(x) = x^3?
  3. How would the graph change if we transformed f(x)=x3f(x) = x^3 (e.g., scaling or translating)?
  4. What happens to the function's values as xx \to \infty or xx \to -\infty?
  5. How do you determine the inflection point of f(x)=x3f(x) = x^3?

Tip: For cubic functions like f(x)=x3f(x) = x^3, the slope of the graph increases as xx increases, causing the curve to steepen.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Cubic Functions

Formulas

f(x) = x^3

Theorems

Basic Function Theorem
Cubic Function Characteristics

Suitable Grade Level

Grades 9-12