Let's say I was asked to sketch a graph that I did not already know the shape of, in an exam or an interview. What methods could I use to do this?
The methods that I know of currently are using f(x) graph transformations. i.e simplifying $$g(x) = 2(x-5)^2 + 7 $$ to something that I know the shape of, like $$f(x) = x^2$$ and transforming it into g(x) by doing $$g(x) = 2f(x-5) + 7$$
I also know that you can plot individual points on a graph, and join them together. I do not know much about this method. One problem that I have with it is that, if the intervals between my points are too large, I may not see certain curves on the graph. If the intervals between my points are too small, I will waste a lot of time during the exam. If you have an effective method of doing this, please share it.
Also, if you have any other methods of sketching graphs, please share them. You can demonstrate it with the function f(x) = 2^(2x-x^2)
Thanks.
For better results:
Try sketching the graph, by taking random well spread points, and finding out the slopes at that point. Hence draw rough lines on the point having slope given by derivative
and draw the curve such that those rough lines are tangents at that point.
Suppose $$f(x)=2^{2x-x^2}$$ Let our points be,$$x=0,1,3,4$$ $$ \begin{array}{c|lcr} x& f(x) & f'(x) \\ \hline 0 &1&1.3 \\ 1 & 2&0\\ 3 &0.12& -0.3\\ 4&0.004&-0.016 \end{array} $$ Roughly drawing lines and points
Me making the graph,
The actual graph superimposed over mine