# Thread: graphical combinations of functions

1. ## graphical combinations of functions

Draw the graph of y = 2x/x^2+1. Use this graph to draw the graph of each function.

a) y = x+3 + 2x/x^2+1
b) y = 2x/x^2+1 - x

2. Originally Posted by checkmarks
Draw the graph of y = 2x/x^2+1. Use this graph to draw the graph of each function.

a) y = x+3 + 2x/x^2+1
b) y = 2x/x^2+1 - x

Hello,

I hope that this post doesn't come too late.

I'll list the steps what you should do to draw the graph of

$y = \underbrace{x+3}_{\text{straight line}} + \underbrace{2x/(x^2+1)}_{\text{function f}}$

1. Draw the graph of

$f(x) = \frac{2x}{x^2+1}$

using a table of x and y-values. (black line)

2. Draw the straight line $y = x+3$ (blue line)

3. Mark points on the graphs which have the same x-value. Measure the y-value of the points placed on the graph of f (black distances). Add these y-values to the y-values of the points placed on the straight line.

4. You'll get a set of points (large red points). Connect these large red points to get the graph of

$y = {\color{blue}x+3} + {\color{black}\frac{2x}{x^2+1}}$

The second problem has to be done in exactly the same way. I'll leave it to you.