The graphs y=3/1+x and y=x are shown below. Determine the coordinates of the points P,Q, and R.?

Question

Here's the graph: http://s07.picshome.com/9f7/img.jpg

I don't even know where to start with this. Can someone solve this and give me their approach. I'd be very greatful.

Thanks a lot

Answer 1

P ( 1/2 , 2 )
Q ( 2 , 2 )
R ( 2, 1)

Solve for P first, then Q, then R.

for the coordinates for P, x is given as 1/2. Plug x=1/2 into the equation y = 3 / (1+x).

Once you get the y-coordinate for P, you'll notice that Q will have the same y-coordinate.

When you get the coordinates for Q, the x-coordinate will be the same for R.

Answer 2

q_midori provided you the best explanation. To add to her comments.

- you are given the first point x=0.5 To find the value in the y=3/(1+x), just substitute for x the value of 0.5. From here you get that y = 2. So, P(x,y) in this case is P=(0.5,2).

- Now you now that the y coordinate of P is 2, so when you project to the point Q, they share the same y value (2). The graph is x=y, so the x value of Q is 2. So, Q(x,y) = (2,2).

- Lastly, with Q now determined, you know that the x coordinate of R is 2. Substituting in y = 3 / (1+x), so will find that the y coordinate of R is 1. Finally, R(x,y) = (2,1).

Go back to the graph and convince yourself that these answers are correct.

Good luck.

Answer 3

x = ?2 ----> vertical asymptote (non-detachable) x = 0 ------> leap discontinuity (non-detachable) x = 2 ------> detachable x = 4 ------> non-detachable observe that there discontinuity at x = 0 is non-detachable even although f(x) is defined at x = 0 ----> f(0) = 4 (as stated in an answer above). A detachable discontinuity has no longer something to do with even if if function is defined at a particular factor, yet has each little thing to do with even if if shrink exists at that factor. considering shrink of f(x) as x procedures 0 from the left = a million/2 and shrink of f(x) as x procedures 0 from the splendid = 4 then shrink of f(x) as x procedures 0 does no longer exist. for this reason discontinuity at x = 0 is non-detachable

Answer 4

p = .5, 2 q = 2,2 r = 2,1