Question

Select the correct answer.

Does the equation below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
y = x^2-9x

Answer 1

As the given equation represents a quadratic function.

Thus,
`y\:=\:x^2-9x` represents a function.

As we know that the function is just a relation in which each input has only one output.

Thus,
`y\:=\:x^2-9x` represents a relation and function.

Explanation:

Given the equation

`y\:=\:x^2-9x`

As the given equation represents a quadratic function.

Thus,
`y\:=\:x^2-9x` represents a function.

As we know that the function is just a relation in which each input has only one output.

Thus,
`y\:=\:x^2-9x` represents a relation and function.

We know that the domain of a function is the set of input or argument values for which the function is real and defined.

`\mathrm{Domain\:of\:}\:x^2-9x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}`

We also know that the range of a function is the set of values of the dependent variable for which a function is defined.

`\mathrm{Range\:of\:}x^2-9x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-(81)/(4)\:\\ \:\mathrm{Interval\:Notation:}&\:[-(81)/(4),\:\infty \:)\end{bmatrix}`

The graph is also attached below. From the graph, it is clear that it represents a Parabola.