## Calculus 8th Edition

(a) $b^{x}=e^{xlnb}$ (b) $(-\infty,\infty)$ (c) $(0,\infty)$ (d) The general shape of the graph of the exponential function for each of the following cases is as depicted in below figure. (i) $b>1$ (ii) $b=1$ (iii) $0 #### Work Step by Step (a) The equation that defines$b^{x}$when b is a positive number and x is a real number must be refers to$ b^{x}=e^{xlnb}$. (b) A function f is a rule that assigns to each element x in a set D exactly one element, called , in a set E. We usually consider functions for which the sets D and E are sets of real numbers. The set D is called the domain of the function. The domain for$f(x)=b^{x}(b>0)$is for all real numbers. Hence,$(-\infty,\infty)$(c) The number$f(x)=b^{x}$is the value of f at x and is read “ f of x.” The range of f is the set of all possible values of as x varies throughout the domain. Hence,$(0,\infty)$(d) The general shape of the graph of the exponential function for each of the following cases is as depicted in below figure. (i)$b>1$(ii)$b = 1$(iii)$0 