SOLUTION: how do you find the domain and range and roots without graphing the queation. We are not allowed to use a graphing calculator, so if I need to graph the problem, how would I do tha

Algebra ->  Rational-functions -> SOLUTION: how do you find the domain and range and roots without graphing the queation. We are not allowed to use a graphing calculator, so if I need to graph the problem, how would I do tha      Log On


   

Question 63988: how do you find the domain and range and roots without graphing the queation. We are not allowed to use a graphing calculator, so if I need to graph the problem, how would I do that? For example: h(x)=sqrt(x^2-6x+8)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
h%28x%29+=+sqrt%28x%5E2-6x%2B8%29
h%28x%29+=+sqrt%28%28x-2%29%28x-4%29%29
Only the positive square root is indicated, so h(x)
can never be negative.
That means the range of h(x) is 0 < h < plus infinity
The values that make h(x) = 0 are the roots, x = 2 and x = 4
Any values of x that make (x-2)(x-4) negative result in
the square root of a negative number and cannot be plotted
(x-2)(x-4) is negative when 2 < x < 4
So, the domain of h is 2 > x > 4
The plot looks like a parabola with everything below the x-axis
missing.