Cube Root Parent Function Flashcards

Questions and Answers

What is the Cube Root Parent Function Equation?

y = x^(1/3) (correct)

y = x^2

y = 3x

y = x^3

What is the graph of the Cube Root Parent Function like?

It is a curve that passes through the origin and extends into the first and third quadrants.

The Cube Root function is strictly increasing.

True

What does the Cube Root ROC indicate?

It increases at a decreasing rate, increases at an increasing rate. Signup and view all the answers

The Cube Root function has a minimum or maximum value.

False Signup and view all the answers

The positive intervals of the Cube Root function are __________.

(0, to infinity) Signup and view all the answers

The negative intervals of the Cube Root function are __________.

(negative infinity to 0) Signup and view all the answers

Study Notes

Cube Root Parent Function Equation

The equation for the cube root parent function is expressed as ( f(x) = \sqrt[3]{x} ).

Cube Root Parent Function Graph

The graph of the cube root function has a characteristic shape that passes through the origin and is symmetrical around the origin.

Cube Root

The cube root function is classified as strictly increasing, meaning that as ( x ) increases, ( f(x) ) also increases without bound.

Cube Root Rate of Change (ROC)

The rate of change of the cube root function is increasing at a decreasing rate initially, but will eventually increase at an increasing rate as ( x ) becomes larger.

Minimum or Maximum?

The cube root function does not have a global minimum or maximum, as it extends infinitely in both directions.

Positive Intervals of Cube Root

The cube root function is positive over the interval ( (0, \infty) ), indicating that it outputs positive values for all positive inputs.

Negative Intervals of Cube Root

The cube root function is defined for negative inputs over the interval ( (-\infty, 0) ), yielding negative output values for negative inputs.

Description

Test your knowledge on the cube root parent function with these flashcards. Explore key concepts like its equation, graph, and characteristics such as monotonicity and rates of change. Perfect for students learning about cubic functions.