Question

Let f be the functio given by f(x)=2x/sqr.(x^2+x+1)?

Answer 1

a.) Find the domain of f. Justify your answers
b.) In the viewing widow provided below, sketch the graph of f.
Viewing Window [-5,5] x [-3,3]
c.) Write an equation for each horizontal asymptote of the graph of f.
d.) Find the range of f. Use f'(x) to justify your answer
Note: f'(x)=(x+2)/(x^2+x+1)^(3/2)

Answer 2

@maxxx

Answer 3

Remember, for denominator, just remember it can't be 0. To put find the domain of f in other words would be then find all x that doesn't make sqrt(x^2+x+1) 0.
For sketching, if the window is [-5,5] you can just put -5, 0, and 5 as the x values (one at a time. so e.g f(-5) = 2(-5) / sqrt((-5)^2-5+1) and then draw the graph.