document.write( "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)\r
\n" ); document.write( "\n" ); document.write( "a, x- and y- intercepts
\n" ); document.write( "b, domain and range
\n" ); document.write( "c, intervals of increase or decrease
\n" ); document.write( "d, minimum or maximum point
\n" ); document.write( "e, equation of the horizontal asymptote \n" ); document.write( "

Algebra.Com's Answer #360562 by KMST(5328) $\"\"$ $\"About$

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$\"y=8%5Ex\"$ , and $\"y=%282%2F7%29%5Ex\"$ are exponential functions.
\n" ); document.write( "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.
\n" ); document.write( "c. Exponential functions with a base greater than 1, like $\"y=8%5Ex\"$ , 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 $\"y=%282%2F7%29%5Ex\"$ 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 $\"y=1\"$ that neither increases nor decreases; it's constant.
\n" ); document.write( "d. and e. Exponential functions with a base other than 1 have the horizontal asymptote $\"y=0\"$ . 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.
\n" ); document.write( "a. Exponential functions are always positive, so they never cross $\"y=0\"$ , the x-axis. They have no x-intercept. They all have a y-intercept, because they have a value for $\"x=0\"$ . 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 $\"x=0\"$ ) at the point (0,1). \n" ); document.write( "

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