Lecture 9: Homework and quiz

Brief review of the lecture

the quiz ?????

The material below was part of the math 1100 course. It may be of some use to students of math 1120, especially those with an interest in computing. It deals with composition of functions.

An assignment statement gives a value to a variable. " x:=4 " is an example. Another example is " x:=x-1 ". We attempt here to give a 'mathematical' meaning to these statements. To do this we construct a function for each statement which describes the value of the variable(s) after the statements execution in terms of the value(s) before. In the first case we get the constant function f(x)=4, and in the second, we get f(x)=x-1.
An example of an IF-THEN_ELSE statement is " if x < 2 then x:=x+1 else x:=2 ".
Several IF-THEN-ELSE statements can be combined.

Let f(x) be defined by the following statement :
If x<=3 the x:=x-3 else x:=2x+4
and g(x) be defined by the statement :
If x>2 then x:=x+1 else x:=2x-1.
Then we may combine the two statements together, starting with f(x), to obtain g(f(x)) =
(x-3)+1 if x<=3 and x-3>2
2(x-3)-1 if x<=3 and x-3<=2
(2x+4)+1 if x>3 and 2x+4>2
2(2x+4)-1 if x>3 and 2x+4<=2

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