If k = {(x, y)|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}. {-5, -3, -1} {0, 2, 4} {5, 7, 9}

The range = {-5 , -3 , -1} ⇒ first answer

Step-by-step explanation:

* In any equation the values of x are the domain of it and

 the values of y are the range of it

* So to find the range of any equation substitute the values

 of x (domain) in the equation to get the corresponding

  values of y (range)

* In the problem

∵ K = {(x , y): x - y = 5}

∵ The domain is {0 , 2 , 4}

* Lets find K(0) , K(2) , K(4)

∵ K(0) = (0) - y = 5

∴ -y = 5 ⇒ Multiply both sides by -1

∴ y = -5

∵ K(2) = (2) - y = 5

∴ 2 - y = 5 ⇒ subtract 2 from both sides

∴ -y = 3 ⇒ Multiply both sides by -1

∴ y = -3

∵ K(4) = (4) - y = 5

∴ 4 - y = 5 ⇒ subtract 4 from both sides

∴ -y = 1 ⇒ Multiply both sides by -1

∴ y = -1

* The range = {-5 , -3 , -1}

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this