Graphing Cube Root Functions

Graphing Cube Root Functions

Assessment

Flashcard

Mathematics

9th - 11th Grade

Practice Problem

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a cube root function?

Back

A cube root function is a function of the form f(x) = ∛(x), which returns the number that, when cubed, gives the input value x.

2.

FLASHCARD QUESTION

Front

What is the general shape of the graph of a cube root function?

Back

The graph of a cube root function is a curve that passes through the origin (0,0) and extends into the first and third quadrants, resembling a sideways S shape.

3.

FLASHCARD QUESTION

Front

How does the graph of f(x) = ∛(x) differ from f(x) = ∛(x - h)?

Back

The graph of f(x) = ∛(x - h) is a horizontal shift of the graph of f(x) = ∛(x) to the right by h units.

4.

FLASHCARD QUESTION

Front

What effect does adding a constant to a cube root function have?

Back

Adding a constant to a cube root function, such as in f(x) = ∛(x) + k, shifts the graph vertically by k units.

5.

FLASHCARD QUESTION

Front

What is the domain of the cube root function f(x) = ∛(x)?

Back

The domain of f(x) = ∛(x) is all real numbers, (-∞, ∞), since you can take the cube root of any real number.

6.

FLASHCARD QUESTION

Front

What is the range of the cube root function f(x) = ∛(x)?

Back

The range of f(x) = ∛(x) is also all real numbers, (-∞, ∞), as the output can be any real number.

7.

FLASHCARD QUESTION

Front

How do you identify the transformations of the graph of a cube root function?

Back

Transformations can be identified by looking at the function's equation: horizontal shifts (x - h), vertical shifts (+k), reflections (negative sign), and stretches/compressions.

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