Answer:
As the given equation represents a quadratic function.
Thus, [tex]y\:=\:x^2-9x[/tex] represents a function.
As we know that the function is just a relation in which each input has only one output.
Thus, [tex]y\:=\:x^2-9x[/tex] represents a relation and function.
Step-by-step explanation:
Given the equation
[tex]y\:=\:x^2-9x[/tex]
As the given equation represents a quadratic function.
Thus, [tex]y\:=\:x^2-9x[/tex] represents a function.
As we know that the function is just a relation in which each input has only one output.
Thus, [tex]y\:=\:x^2-9x[/tex] 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.
[tex]\mathrm{Domain\:of\:}\:x^2-9x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
We also know that the range of a function is the set of values of the dependent variable for which a function is defined.
[tex]\mathrm{Range\:of\:}x^2-9x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:-\frac{81}{4}\:\\ \:\mathrm{Interval\:Notation:}&\:[-\frac{81}{4},\:\infty \:)\end{bmatrix}[/tex]
The graph is also attached below. From the graph, it is clear that it represents a Parabola.
