5.3 Polynomial Functions, Graphs, and Composition

Evaluating Polynomial Functions Example 1 Evaluating Polynomial Functions Answer

Using a Polynomial Model to Approximate Data Example 2 The number of U.S. households estimated to see and pay at least one bill on-line each month during the years 2000 through 2006 can be modeled by the polynomial function where x = 0 corresponds to the year 2000, x = 1 corresponds to 2001, and P(x) is in millions. Use this function to approximate the number of households that paid at least one bill on-line each month in 2006.

Using a Polynomial Model to Approximate Data (continued) Example 2 Answer Since x = 6 corresponds to 2006, we must find P(6). According to this model, in 2006, about 45.34 million households paid at least one bill on-line each month.

Adding and Subtracting Functions Example 3 Adding and Subtracting Functions Let and Find each function. (a) (f + g)(x) (b) (f – g)(x) Answer (a)

Adding and Subtracting Functions (continued) Example 3 Adding and Subtracting Functions (continued) (b)

Adding and Subtracting Functions Example 4 Adding and Subtracting Functions For and find each of the following. (a) (f + g)(x) and (f + g)(–1) (b) (f – g)(x) and (f – g)(1) Answer (a)

Adding and Subtracting Functions (continued) Example 4 Adding and Subtracting Functions (continued) (b)

Finding a Composite Function Example 5 Finding a Composite Function Answer

Finding Composite Functions Example 6 Finding Composite Functions Find the following. (a) (b) Answer (a) (b)

Graphing Variations of the Identity, Squaring, and Cubing Functions Example 7 Graph Give the domain and range. Answer Create a table of values. x f(x) = –2x2 –2 –8 –1 1 2

Graphing Variations of the Identity, Squaring, and Cubing Functions (continued) Example 7 Plot the points and join them with a curve.

Graphing Variations of the Identity, Squaring, and Cubing Functions (continued) Example 7 Any value of x can be used, so the domain is The maximum y-value is 0 and there is no minimum y-value, so the range is