Match it with its graph (choices are labelled A to L ), and...

Match it with its graph (choices are labelled $A$ to $L$ ), and b) state whether or not the equation represents a function - with a justification. Assume that $x$ is the independent variable and $y$ is the dependent variable.
$$y^{3}=x$$
(graph cannot copy)

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Key Concepts

Cube Root Function

The cube root function is defined as the inverse of raising a number to the third power, meaning it takes an input and returns the unique real number that, when cubed, equals that input. This function is continuous over all real numbers and is inherently one-to-one, ensuring that each input corresponds to exactly one output.

Vertical Line Test

The vertical line test is a graphical method for determining whether a relation represents a function. If no vertical line can intersect the graph at more than one point, then the graph represents a function. This test is crucial because it visually confirms that each input in the domain is associated with only one output.

Function Definition

A function is a type of relation where each independent variable is paired with exactly one dependent variable. Even if an equation is presented in an implicit form, one must check that it can be rearranged or interpreted such that every input has a unique output, thereby satisfying the definition of a function.

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