Addition of ordinates

[Stick]

I absolutely hate addition of ordinates. I hate having to slide my ruler across a graph and adding the y values. It's even worse when it's a textbook question and you don't have any grid paper to guide you.

There has to be a better, quicker and more effective way to these questions. I like using a table of values, but obviously this just isn't feasible for some of the graphs that you'll get (it would probably suffice for Methods though). Any techniques to make this a less painful experience would be greatly appreciated. I am aware of the Specialist technique where the horizontal asymptote is transformed to become the expression following the hyperbola/truncus.

[Randall]

I absolutely hate addition of ordinates. I hate having to slide my ruler across a graph and adding the y values. It's even worse when it's a textbook question and you don't have any grid paper to guide you.

There has to be a better, quicker and more effective way to these questions. I like using a table of values, but obviously this just isn't feasible for some of the graphs that you'll get (it would probably suffice for Methods though). Any techniques to make this a less painful experience would be greatly appreciated. I am aware of the Specialist technique where the horizontal asymptote is transformed to become the expression following the hyperbola/truncus.

Hi Stick, I did Methods 3/4 last year,
What you describe is essentially all you need to know. Method [1] is to use your ruler (or just use the 'finger' method, use your thumb and index finger to measure the gap between two points) and Method [2] is to analyse the function itself and generalise it to recognisable form if it is possible.

The priorities in this regard are that you can draw a reasonably accurate graph using additional of ordinates given two scaled functions. If the function isn't one of a general form that you recognise, then you may have to use calculus to find a turning point, and the absolute maximum and minimum values. Addition of ordinates is really a pain if you do it tech-free. In a tech-able assessment, you can get draw the graph on your CAS and you will have a clear idea of the shape.

If done carefully and properly, it is a slow technique (and an inefficient one). So that suggests to me that you have it down!
Hope this helps.

[TrueTears]

general graph sketching method exert from stewarts calculus, any almost any curve in R^2 can be sketched with these few steps.

no need for any "addition of ordinates" bullshit