Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

Vertical asymptote:

Horizontal asymptote:

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

One root,

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

Roots of f(x) means the value of x where f(x) = 0

One root,

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x)

For all, other values of , is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is .

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) .

It is possible only when

vertical asymptote:

Horizontal Asymptote is the value of f(x) , where value of x .

Horizontal asymptote:

Please refer to the graph of given function as shown in the attached image.

i'm sorry i don't know

step-by-step explanation:

it would open into a square depending on the type of envelope i’m not sure about the second part