Question

Select the correct answer.

Answer 1

Answer:

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.

Step-by-step 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.

$\mathrm{Domain\:of\:}\:x^2-9x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

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

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

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