Question

given that the graphs of and intersect at and there is one point where the graphs of and must intersect. what is the sum of the coordinates of that point?

Answer 1

The sum of the coordinates of these points is 204.

Since the graphs of y= h(x) and y= i(x) intersect at (2,2), (4,6), and (6, 12), we know that these are the x-coordinates of the three points where the graphs intersect. To find the y-coordinates of these points, we can plug the x-coordinates into the respective equations.

For y= h(x), we have:

h(2) = y

h(4) = 6

h(6) = 12

For y= i(x), we have:

i(2) = y

i(4) = 6

i(6) = 12

The question states that there is one point where the graphs of y= h(2x) and y= 2j(x) must intersect. This means that there is one x-value for which both equations are equal. To find this x-value, we can set the two equations equal to each other:

h(2x) = 2j(x)

We can plug in the x-coordinates that we know from the first part of the question:

h(2(2)) = 2j(2)

h(4) = 2j(2)

h(2(4)) = 2j(4)

h(8) = 2j(4)

h(2(6)) = 2j(6)

h(12) = 2j(6)

We can now solve for the y-coordinates of these points:

y = 2j(2)

y = 18

y = 2j(4)

y = 48

y = 2j(6)

y = 144

The sum of the coordinates of these points is 204.

Question

given that the graphs of y= h(x) and y= i(x) intersect at (2,2) , (4,6), (6, 12) and there is one point where the graphs of y= h (2x) and y= 2j(x) must intersect. what is the sum of the coordinates of that point?