Question

C = 200 – 7x + 0.345x2

Answer 1

The way to find the domain and the range is illustrated below.

How to illustrate the information?

From the information, c(x) = 200 - 7x + 0.345x². It should be noted that the domain is the set of x-values that are feasible.

The range is the set of possible results for c(x). They are the possible costs. You can derive this from the fact that c(x) is a parabola and you can draw it, for which you can find the vertex of the parabola, the roots, the y-intercept, the shape.

You can substitute some values for x to help you, for example:

x      y

0    200

1    200 -7 +0.345 = 193.345

2    200 - 14 + .345 (4) = 187.38

3    200 - 21 + .345(9) = 182.105

4    200 - 28 + .345(16) = 177.52

5    200 - 35 + 0.345(25) = 173.625

6    200 - 42 + 0.345(36) = 170.42

10  200 - 70 + 0.345(100) =164.5

11 200 - 77 + 0.345(121) = 164.745

If the functions do not have real roots, then the costs never decrease to 0. The function starts at c(x) = 200, decreases until the vertex, (x =10, c=164.5) and starts to increase.

Then the range goes from 164.5 to infinity, limited to the solution for x = positive integers.

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Complete question:

the daily production cost, c, for x units is modeled by the equation: c = 200 – 7x 0.345x² explains how to find the domain and range of c.