SOLUTION: 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)

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.
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

The basic exponential function with base 4 is (red):

Compressed horizontally by a factor of 1/3 means the exponent has been multiplied by 3 to give (green):

Reflected in the x-axis changes each y value to its opposite; that means the function has been multiplied by -1, to give (blue):

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 , or (purple):

The y-intercept is supposed to be (0,2), which it is, so our equation is good.

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.
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