document.write( "Question 1138871: An exponential function with a base of 4 has been compressed horizontally by a factor of 1/3 and reflected in the x-axis. Its asymptote is the line y = 3. Its y-intercept is (0, 2). Write an equation of the function. \n" ); document.write( "
Algebra.Com's Answer #756671 by greenestamps(13216)\"\" \"About 
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\n" ); document.write( "The basic exponential function with base 4 is \"y=4%5Ex\" (red):

\n" ); document.write( "\"graph%28400%2C400%2C-.5%2C.5%2C-5%2C5%2C4%5Ex%29\"

\n" ); document.write( "Compressed horizontally by a factor of 1/3 means the exponent has been multiplied by 3 to give \"y+=+4%5E%283x%29\" (green):

\n" ); document.write( "\"graph%28400%2C400%2C-.5%2C.5%2C-5%2C5%2C4%5Ex%2C4%5E%283x%29%29\"

\n" ); document.write( "Reflected in the x-axis changes each y value to its opposite; that means the function has been multiplied by -1, to give \"y+=+-4%5E%283x%29\" (blue):

\n" ); document.write( "\"graph%28400%2C400%2C-.5%2C.5%2C-5%2C5%2C4%5Ex%2C4%5E%283x%29%2C-4%5E%283x%29%29\"

\n" ); document.write( "With the asymptote at y=3, the whole graph has been moved up 3 units, moving the asymptote from y=0 to y=3, to give \"y+=+-4%5E%283x%29%2B3\", or \"y+=+3-4%5E%283x%29\" (purple):

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\n" ); document.write( "The y-intercept is supposed to be (0,2), which it is, so our equation is good.

\n" ); document.write( "If the y-intercept had not been as desired, the equation would have involved a coefficient on the 4^(3x) term; and that would have moved the y-intercept, making the determination of the function more difficult. \n" ); document.write( "
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