Suppose that g is defined as g(x) = -6(x-2)^2-2 what is the range?

Question

asnaseer · Answer

this site might help you understand range and its related concepts of domain and co-domain: http://www.mathsisfun.com/sets/domain-range-codomain.html

anonymous · Answer

yes i understand what domain and range are i just dont understand how you connect it to a number line??

asnaseer · Answer

look at the function you were given:$$g(x)=-6(x-2)^2-2$$notice the term $(x-2)^2$ will ALWAYS be positive, so its value will range from 0 to $\infty$, agreed?

anonymous · Answer

yes so its not range is less than or equal -2

asnaseer · Answer

so maximum value of g(x) will be when $(x-2)^2=0$ which gives g(x)=-2.
so g(x) ranges from -2 to -infinity

asnaseer · Answer

$$-\infty<g(x)\le-2$$

anonymous · Answer

so on number line i would put a closed circle on -2 and then have a line go infinitely onto the negative direction

asnaseer · Answer

precisely - you got it!

anonymous · Answer

thnks

asnaseer · Answer

yw :)