y = $a^x$ (a > 1): passes through (0,1), increasing, concave up, horizontal asymptote y = 0 on the left. y = $a^x$ (0 < a < 1): passes through (0,1), decreasing, concave up, horizontal asymptote y = 0 on the right. y = $log_a$(x) (a > 1): passes through (1,0), increasing, concave down, vertical asymptote x = 0. y = $log_a$(x) (0 < a < 1): passes through (1,0), decreasing, concave up, vertical asymptote x = 0. The exponential and log graphs are reflections across y = x. JEE uses graph-based reasoning for inequality problems and for determining the number of solutions of equations like 2^x = x+1.