Equivalent expressions of functions Families of functions The examples below present linear functions in graph and correspondence rule forms. For each given function, construct a family of functions all of which have a certain common property (some examples of functions in these families are also plotted in the figures). You will find it useful to first construct an equivalent correspondence rule for the given function, which emphasizes the common property. f Construct a family of functions containing f(x), so that all the functions have a common point of intersection with the y-axis. g Construct a family of functions containing g(x), so that all the functions have a common point of intersection with the x-axis. h Construct a family of functions containing h(x), so that all their graphs pass through the given point.

The form f(x)=ax+b The form f(x)=a(x-c) The form f(x)=a(x-c)+m Emphasizing information Emphasizing intersections Families of functions Features from value tables Partial pictures Equivalent recipes Telephone rates Verbal descriptions of equivalent expressions Stories Describing a trip Speeding car Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9 Exercise 10 Exercise 11 Exercise 12 Exercise 13 Exercise 14 Exercise 15 Exercise 16 Exercise 17 Exercise 18 Exercise 19