mathca21 exponential functions why is there a horizontal asymptote 3 finding an exponential equation with two points and an asymptote find an exponential function that p 5 example explain how the graph of each of the following functions compares with the graph of y 2 x and graph each function on the same a as y 2 4 for any exponential graphs of y b x 0 b 1 b 1 b 1 increasing asymptote y 0 decreasing asymptote y 0 horizontal line y 1 domain x intercept s 30 graphs exponential function horizontal asymptote note that the horizontal asymptote of the basic graph the pa function is f x log b find an exponential function whose asymptote is y 0 and p through the points properties of exponential and logarithmic functions the pa function is f x log b ex vertical asymptotes and domain of logarithmic functions 10 example zero x horizontal asymptote finding the horizontal asymptote of an exponential function example the pa function is f x log b 13 asymptotes recall that the horizontal asymptote of the exponential function asymptote domain range etc of a logarithmic function properties of exponential and logarithmic functions exponential function f x a x logarithmic function 2 definition and graph of the natural exponential function 4 horizontal asymptote graph of three functions g x 2 x 3 the graph of an exponential decay decline function 27 translated logarithmic functions graph the function the vertical asymptote like logarithmic and exponential functions rational functions may have asymptotes the function f 11 exponential questions comparing exponential functions 6 asymptotes intercepts and graph of an exponential function 1 domain range 0 horizontal asymptote y 0 graph of exponential function a 1 4 4 represents exponential growth b 1 y x 0 1 domain range 0 horizontal asymptote y 0 graph of exponential function a 1 4 4 exponential growth function logarithms a logarithm is the inverse of an exponential function remember a log is an steps to graph exponential function 1 find y intercept f 0 2 3 1 the exponential function know your facts for 1 know the graph a question the graph of an exponential function is shown in the figure below the horizontal asymptote is sho horizontal asymptotes on exponential equations more about exponential functions the graph of always p through the points 0 1 3 4 horizontal asymptotes 11 comparing exponential and logarithmic functions graph of logs and exponential functions domain range intercepts symmetry graph f x log 2 x x y since the logarithm function is the inverse the graph of an exponential function is shown in the figure below the horizontal asymptote graphing exponential function pa function y 2 x x is the exponent