Question

C = 200 – 7x + 0.345x2 find the domain and range of C.

Answer 1

Domain:
`(-\infty,\infty)`

Range:
`[164.493,\infty)`

Explanation:

The domain is all x-values. Since it doesn't matter what you put in for x, all real numbers work.

The range is all y-values. Since the leading coefficient of 0.345 is positive, this means we need to find the absolute minimum by using the formula
`x=-(b)/(2a)` and then determining what C is given the value of x:

`x=-(b)/(2a)`

`x=-(-7)/(2(0.345))`

`x\approx10.145`

Therefore:

`C=200-7x+0.345x^2`

`C=200-7(10.145)+0.345(10.145)^2`

`C\approx164.493` is the absolute minimum