Find the domain and range of y=2-5/(x-4)

Domain is all real numbers except 4.

Range is all real numbers except 2.

Step-by-step explanation:

You can find the domain by taking the denominator and setting it equal to 0 and then solving for x.

x-4=0

Add 4 to both sides

x=4

So, x cannot equal 4 in the domain.

You can find the range by using the inverse of the function, which means you flip the x and y.

x=2-5/(y-4)

Then you have to solve for y. Start by subtracting 2 from both sides.

x-2=-5/(y-4)

Multiply (y-4) to both sides.

(x-2)(y-4)=-5

Then divide (x-2) from both sides.

y-4=-5/(x-2)

Add 4 to both sides.

y=4-5/(x-2)

Then do the same as the domain and take the denominator and set it equal to 0 and solve for x.

x-2=0

Add 2 to both sides.

x=2

So the range cannot equal 2.