Students will identify appropriate input values (domain)
and output values (range), determine inputs for which the function values
increase, decrease or remain constant, find inputs resulting in a maximum
or a minimum output value, and when needed, identify inputs which result
in outputs that are less than or greater than a given value. Related equations
and inequalities will be solved when analysis and meaningful interpretation
necessitates such algebraic methods.
Example A. The following graph represents the sales over several years for the Amexro Company. Use this graph to answer the following questions. Assume that the labels identify the locations needed.
1. Between what years did the sales increase? _______________________________________________
2. Between what years did the sales decrease? _______________________________________________
3. Between what years were the sales constant? ______________________________________________
4. For what year(s) were the sales $10,000,000? ______________________________________________
5. In what year were the largest sales recorded? _____________________________________________
Example B. The following graph is of the function y = f(x). Use this graph to answer the following questions. Assume that the labels identify the locations needed.
1. State the interval(s) on which f increases. _______________________________________________
2. State the interval(s) on which f decreases. _______________________________________________
3. State the interval(s) on which f is constant. ______________________________________________
4. For what value(s) of x is f(x) = 45? ______________________________________________________
5. What is the minimum value of f ? ______________________________________________________
6. For what value of x is f(x) a minimum? __________________________________________________