Math Problem Statement

Identify the domain and then graph the function. f left parenthesis x right parenthesis equals RootIndex 3 StartRoot x EndRoot plus 2

Solution

The graph of the function f(x)=x3+2f(x) = \sqrt[3]{x} + 2 is shown above. As expected, the graph is a shifted version of the basic cube root function, translated 2 units upward.

Would you like more details or have any questions about this topic?

Here are five related questions you might find interesting:

  1. How do translations affect the graph of a general function?
  2. What is the difference between the cube root function and the square root function in terms of their domains and ranges?
  3. How do you determine the range of the function f(x)=x3+2f(x) = \sqrt[3]{x} + 2?
  4. What are the key points that you should plot when sketching the graph of a cube root function?
  5. How would the graph change if we multiplied the cube root by a constant before adding 2?

Tip: When graphing functions, always consider transformations like shifts, stretches, and reflections to understand how the basic function's shape changes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Cube Root Functions
Graphing

Formulas

f(x) = ∛x + 2

Theorems

Domain and Range of Cube Root Functions
Transformations of Functions

Suitable Grade Level

Grades 9-12