Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex][164.493,\infty)[/tex]
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 [tex]x=-\frac{b}{2a}[/tex] and then determining what C is given the value of x:
[tex]x=-\frac{b}{2a}[/tex]
[tex]x=-\frac{-7}{2(0.345)}[/tex]
[tex]x\approx10.145[/tex]
Therefore:
[tex]C=200-7x+0.345x^2[/tex]
[tex]C=200-7(10.145)+0.345(10.145)^2[/tex]
[tex]C\approx164.493[/tex] is the absolute minimum
