Part 1: Graph piecewise functions from tables and equations.

Question

Isabel’s competition,who sells books and no other products, charges a shipping fee of $1.99 per book plus a fixed fee of $3 for each order. Let x be the number of books purchased and f(x) be the price of shipping one order of books. Write a function that expresses f(x) and explain the value of f(x) for x = 0.

Graph the function in part e.

Is your graph discrete or continuous? Explain.

Answer 1

f(x) = 1.99x + 3 is the cost fuction for customers, and the revenue function for the seller

x=0 means zero books, so no need for a $3 shipping fee, as nothing is being shipped

so the step function is

f(x) = 1.99x +3 for x>0

f(x) = 0 for x = 0

where x is any positive integer

the graph is a point at the origin (0,0), then points (1, 4.99), (2, 6.98), (3, 10.97), (4, 14.96), (5, 18.95), ... (x, 1.99x+3)

The graph is discontinuous, discrete, with a jump from x=0 to x=1, from y=0 to y=4.99

for x=1 to all x>1, the points are all disontinuous, but all lie on a straight line with slope = 1.99 and y intercept =3