Choose the domain for which each function is defined

Part 1) ----->

Part 2) ---->

Part 3)   ----> All real numbers

Part 4) ---->

Step-by-step explanation:

we know that

The domain of a function is the set of all possible values of x

Part 1) we have

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=0 the function is not defined

therefore

The domain is

Part 2) we have

we know that

In a quotient the denominator cannot be equal to zero

so

For the value of x=-4 the function is not defined

therefore

The domain is

Part 3) we have

Applying the distributive property

This is a vertical parabola open upward

The function is defined by all the values of x

therefore

The domain is all real numbers

Part 4) we have

we know that

In a quotient the denominator cannot be equal to zero

so

Equate the denominator to zero

Remember that

(

The solution is x=-4

so

For the value of x=-4 the function is not defined

therefore

The domain is

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

the area of the rectangle is 35units^2.

step-by-step explanation:

graph it and find the distance.

it is a 5*7 rectangle.

therefore the area is 35units^2.