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Question 552897: Without graphing state the following for the graph of the exponential functions; y=8^x, y=(2/7)^x(2 over 7 is the fraction)
a, x- and y- intercepts
b, domain and range
c, intervals of increase or decrease
d, minimum or maximum point
e, equation of the horizontal asymptote
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  , and are exponential functions.
b. The domain of an exponential function is the entire set of real numbers. There is always a value for any power of a positive real number.
c. Exponential functions with a base greater than 1, like , increase throughout their domain. We encounter that kind of function in cases of exponential growth. Exponential functions with a base lesser than 1, like and decrease throughout their domain. We encounter that kind of function in cases of exponential decay. If the base was 1, it would be the very boring function  that neither increases nor decreases; it's constant.
d. and e. Exponential functions with a base other than 1 have the horizontal asymptote  . They either approach zero as x increases (if the base is lesser than 1), or approach zero as x tends to -infinity. There is no minimum or maximum point, because the functions increase, decrease, or are constant throughout their domain, as stated in c. above.
a. Exponential functions are always positive, so they never cross , the x-axis. They have no x-intercept. They all have a y-intercept, because they have a value for  . That value is 1, for any positive real base. So y=1, is the y-intercept. Both given functions (an all exponential functions) cross the y-axis (the line ) at the point (0,1).
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