Discovering Exponential Functions: 2 Equations for y=3 with y-intercept of 5

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To create two equations for an exponential function with a y-intercept of 5 and an asymptote at y=3, one equation provided is y=2^(x+1) + 3. To find a second equation, the suggestion is to reflect the graph across the y-axis by replacing "x" with "-x". This transformation yields the second equation, which maintains the same characteristics. Both equations represent the same exponential function with the specified properties. Understanding these transformations is crucial for working with exponential functions.
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I need to write 2 equations that represent the same exponential function with a y-intercept of 5 and an asymptote at y=3. I got y=2^(x+1) + 3 but I don't know how to find the second equation. Can someone please explain this to me. Thanks.
 
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Since the y- intercept is at (0, 5) and the asymptote, y= 3, is symmetric about the x-axis, try "reflecting" that graph in the y-axis. That is, replace your "x" with "-x".
 
Thank you!
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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