mathca21 exponential functions why is there a horizontal asymptote exponential and logarithmic functions 3 finding an exponential equation with two points and an asymptote find an exponential function that p note that the horizontal asymptote of the basic graph 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 exponential function horizontal asymptote 30 graphs finding an exponential equation with two points and an asymptote find an exponential function that p 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 the pa function is f x log b horizontal note exponential functions have horizontal asymptotes 10 example zero x horizontal asymptote properties of exponential and logarithmic functions ex vertical asymptotes and domain of logarithmic functions asymptote domain range etc of a logarithmic function 11 exponential questions 1 identify horizontal asymptote y c 6 asymptotes 11 comparing exponential and logarithmic functions intercepts and graph of an exponential function graph of three functions g x 2 x 3 the graph of an exponential decay decline function 3 1 the exponential function know your facts for 1 know the graph a 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 steps to graph exponential function 1 find y intercept f 0 2 horizontal asymptotes on exponential equations for the function determine the following if it exists how to find the horizontal asymptotes of exponential equations graph of logs and exponential functions domain range intercepts symmetry finding the horizontal asymptote of an exponential function example 3 graph of f x x 2 x 3 6 5 the graph of f x b x 0 b 1 y x 0 1 domain range 0 horizontal asymptote y 0 graph of exponential function 0 a 1 4 8 characteristics about the graph of an exponential function a 1 1 graph f x log 2 x x y since the logarithm function is the inverse 13 summary 6 exponential functions 4 horizontal asymptote 13 asymptotes recall that the horizontal asymptote of the exponential function