For problems a b c and d find 1 The equation for the horizon

For problems a, b, c, and d, find 1.) The equation for the horizontal asymptote of the given function and (2.) the domain and range of the given function

a.) f(x) = 3^{x - 2}       equation for horiontal aymptote of the given function________   Domain_________Range________

b.) g(x) = 3^x - 4    equation for horizontal asymptote of the given function________Domain__________Range________

c.) h(x) = -e^x           equation for the horizontal asymptote of the given function_________Domain_________Range____________

d.) f(x) -e^-x + 2      equation for the horizontal asymptote of the given function_________Domain_________Range___________

Solution

a) f(x) = 3x - 2

no horizontal asymptote exist

domain = R, range = R

b) g(x) = 3x - 4

no horizontal asymptote exist

domain = R, range = R

c) h(x) = -e^x

horizontal asymptote => y = 0

Domain = R , range = (-infinity, 0)

d) f(x) = -e^-x + 2

horizontal asymptote => y = 2

Domain = R,, range = (-infinity,2)