Question

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

Answer 1

Answer:

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

Range: $[164.493,\infty)$

Step-by-step 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 $x=-\frac{b}{2a}$ and then determining what C is given the value of x:

$x=-\frac{b}{2a}$

$x=-\frac{-7}{2(0.345)}$

$x\approx10.145$

Therefore:

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

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

$C\approx164.493$ is the absolute minimum