Use a graphing utility to graph the function. Find the domain and range of the function. (Enter your answers using interval notation.) f(x)= √x²+4

Question

Use a graphing utility to graph the function. Find the domain and range of the function. (Enter your answers using interval notation.) f(x)= √x²+4

Answer 1

f(x) = y= sqr(x^2 +4)

range is y>0 y is in the interval [0,infinity)

domain is all real numbers, x is in the interval (-inf,+inf)

it's a hyperbola or top half of it, one branch of it in quadrant 1 and 2, with vertex = min point = (0,2), symmetrical about the y axis.

y^2= x^2 +4

x^2 -y^2 = 4 is the full hyperbola, with both branches, symmetrical about both axes

asymptotes are y =+/-x

two diagonal lines intersecting at the origin