1119

http://www.vhcc.edu/dsmith/images/graph_series_1.htm

Give the formula for a polynomial function which passes through the points (-3, 0), (2, 0) and (5, 0), having a y-intercept of 4.

We can get the points on the x axis from (x+3)(x-2)(x-5).

The y-intercept of (x+3)(x-2)(x-5) is 30 and we want a y-intercept of 4.  So we vertically stretch by factor 4/30 to get

What are the possible shapes of the graph of a degree-4 polynomial?

(x-2)(x-1)(x+1)(x+3)

(x-2)^2(x-1)(x+3)

(x-1)^3(x+3)

(x-1)^4

(x-1)^2(x+3)^2

(x-2)(x+3)(x^2+x+2)

(x-1)^2(x^2+x+2)

Sketch graphs of f(x) = (x - 3) and g(x) = (x+ 2).

For the functions f(x) and g(x) of the preceding problem

For the functions f(x) and g(x) of the preceding problem