MA005: Calculus I

Functions are abstract structures, but sometimes it is easier to think of them in a more concrete way. One way is to imagine that a function is a special purpose computer, a machine which accepts inputs, does something to those inputs according to the defining rule, and produces an output. The output is the value of the function for the given input value. If the defining rule for a function $f$ is "multiply the input by itself" , $f \; (input) = (input)(input)$ , then Fig. 1 shows the results of putting the inputs $x, 5, a, c + 3$ and $x + h$ into the machine $f$.

Practice 1: If we have a function machine g whose rule is "divide 3 by the input and add 1", $g(x) = 3/x + 1$, what outputs do we get from the inputs $x, 5, a, c + 3$ and $x + h$ ? What happens if we put 0 into the machine $g$?

You expect your calculator to behave as a function: each time you press the same input sequence of keys you expect to see the same output display. In fact, if your calculator did not produce the same output each time you would need a new calculator. (On many calculators there is a key which does not produce the same output each time you press it. Which key is that?)