Graphs How to draw graphs

Asymptotes An asymptote is a horizontal/vertical line which a graphical function tends towards but does not touch, it is represented as a dotted line on a graph 3 In this case x=3 is the vertical asymptote

Calculating Vertical Asymptotes To calculate the vertical asymptote we must find what value x is as y tends towards infinity. To calculate this the denominator in this case (x+2) must be equal to 0 as when any number is divided by 0 the result is ∞ for example so to calculate the vertical asymptotes each bracket on the denominator is made equal to 0 so x+2=0 therefore x=-2 and the vertical asymptote is at -2.

Horizontal Asymptotes To calculate the horizontal asymptote. Take the largest power from above and below which in this case. Now you have just learnt how to calculate the vertical asymptotes so do it now Don’t just click on, calculate the Vertical asymptotes NOW This then cancels to which means the horizontal asymptote is 1. If you got the asymptotes as 2 and -2 then you are correct

Where the Graph crosses the axis The next step is to find where the graph crosses the axis When x=0 the y co-ordinate is 0 and in this case the graph doesn’t cross the x axis.

Does the line tend from above or below? In order to see if the graph tends from above or below we must sub in large positive and negative values of x usually 100/-100.

Then Draw the Graph