Determine the Domain the vertical Asymptotes and the horizon

Determine the Domain the vertical Asymptotes and the horizontal Asymptote for each of the following: R(x) = 2x + 4/3x^2 - 12; R(z) = 3x^2/x^2 + 4x - 21. Find the coordinates of the vertex for y = f(x) = -2(x - 5)^2 - 7. Find the maximum value of the function f(x) = -4x^2 - 12x + 15. Determine (f g)(x) and (g f)(x) in each of the following: f(x) = x^2 and g(x) = x+ 2 f(x) = Squareroot x - 1 and g(x) = x^3 + 1.[Determine the domain of (g f)(x)]. Determine the inverse in each of the following and prove the result: f(x) = 4x + 3; g(x) = 5x/x - 2; h(x) = 2 Squarerrot x + 1 + 3 Show that f(x) = 9/5 x + 32 and g(x) = 5/9(x - 32) are inverse of each other. If f(x) = 2/x + 3 and g(x) = 3/x - 4, find the domain of (f g)(x). Let f(x) = {-3, x 2 Find f(1), f(-3) and f(4) Sketch the graph and determine the domain and range of f(x)

Solution

2) a) Domain = (x < -2 or -2 < x < 2 or x > 2)

Horizontal asymptotes = y = 0

vertical asymptotes = x = 2, x = -2

b) Domain = (x < -7 or -7 < x < 3 or x > 3)

Horizontal asymptotes = y = 3

vertical asymptotes = x = -7, x = 3