Functions and Their Graphs
Read this section for an introduction to functions and their graphs. Work through practice problems 1-5.
A Graph from an Equation
Creating the graph of a function given by an equation is similar to creating one from a table of values - we need to plot enough points where so we can be confident of the shape and location of the graph of the entire
function. We can find a point which satisfies ) by picking a value for and then calculating the value for by evaluating . Then we can enter the
value in a table or simply plot the point .
If you recognize the form of the equation and know something about the shape of graphs of that form, you may not have to plot many points. If you do not recognize the
form of the equation then you will have to plot more points, maybe 10 or 20 or 234: it depends on how complicated the graph appears and on how important it is to you (or your boss) to have an accurate graph. Evaluating at a lot of different values for and then plotting the points is usually not very difficult, but it can be very time–consuming. Fortunately, there are now calculators and personal computers which will
do the evaluations and plotting for you.