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.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.