Question 884127
one way is to graph it.
that should tell you what value is not possible.


the other way is to use logic or just solve the equation for each of the values indicated to see which value is not possible.


if the value is possible it is within the range.


if the value is not possible it is not within the range.


you can also see right off that bat that (x-2)^2 has to be positive.


it can't be negative because (-x)^2 = (-x) * (-x) = x^2


that points to -3 as not being possible.


let's see if we can prove that by solving the equation for f(x) = -3


we get 7(x-2)^2 = -3
divide both sides of this equation by 7 to get:
(x-2)^2 = -3/7
take the square root of both sides of this equation to get:
x-2 = +/- sqrt(-3/7)
since you cannot take the square root of a negative number and get a real number answer, then selection c is the one that is not possible.


the graph of this equation looks like this:


{{{graph(400,400,-1,6,-5,20,7(x-2)^2)}}}


looking at the graph you can see that it never gets below 0.


the range is all values of x >= 0.