HOW TO FORM FUNCTION THAT DECREASES THEN REMAIN CONSTANT.

Question

I want to form a price function, so there is x(the unit of products) and the y(the price of each unit). As x increases, y decreases, but only until x=10, because after x=10, the y will remain constant at y=21 regardless of the increasing x. I just wanna know is it possible to form a function for this type of graph.

Answer 1

I drew a plot of this piecewise function, but it was too much data and was not allowed for an answer. So I will try to describe it the best I can here.

For 0 units, there is no price per unit, so the graph would start at U = 1 for 1 Unit. Suppose that 1 Unit results in a Price / Unit of $A. Also suppose that the graph would be linear between U = 1 and U = 10.

P (1) = $A

P (10) = $21

Taking the slope of these two points, the plot between 1 and 10 would have a slope of

( $A - $21 ) / (1 - 10) = $29 / -9 = -($21 - A) / - 9 = ($21 - $A) / 9

Price / Unit = P

(($21 - $A) / 9)*U + $A for 1 <= U < 10

P =

$21 for U > 10

Answer 2

y = kx, for x ≤10

y = x, for x > 10

It is called a "piece-wise" function.