Question

Where is the horizontal asymptote of the graph of y=3(2/3)^x-1

Answer 1

@Nnesha

Answer 2

for say any exponential function, with only "x" as exponent, where do they have their horizontal asymptote?
like say \(\large 2^x\ or \ 3^x?\)

Answer 3

The horizontalassymptote would be 2or 3

Answer 4

@pooja195

Answer 5

@jdoe0001 is helping you already :)

Answer 6

you see
the horizontal asymptote for that function, is the same as for any exponential function
the only difference is the (x-1) <--- which is just a function transformation
to be exact, is a horizontal shift from the "parent" function

Answer 7

sois it 2/3

Answer 8

hmm nope, that's just the base
not the horizontal asymptote

Answer 9

so it is -1

Answer 10

notice all these exponential functions -> http://www.softmath.com/tutorials-3/relations/articles_imgs/2441/expone60.gif

they all have the same horizontal asymptote
though some are steeper than others
the horizontal asymptote is the same

anyhow.. need to dash but to get the transformation

\(\large {
\textit{function transformations}
\\ \quad \\

\begin{array}{llll}

\begin{array}{llll} shrink\ or\\ expand\\ by\ {\color{purple}{ A}}\end{array}
\qquad
\begin{array}{llll} vertical\\ shift\\ by \ {\color{green}{ D}} \end{array}

\begin{array}{llll}{\color{green}{ D}} > 0& Upwards\\ {\color{green}{ D}} < 0 & Downwards\end{array}
\\

% template start
\qquad \downarrow\qquad\qquad\quad\ \downarrow\\
y = {\color{purple}{ A}} ( x + {\color{red}{ C}} ) + {\color{green}{ D}}\\
%template end
\qquad\qquad \quad \uparrow \\

\qquad\begin{array}{llll} horizontal\\ shift\\ by \ {\color{red}{ C}}\end{array}

\begin{array}{llll}{\color{red}{ C}} > 0 & to\ the\ left\\ {\color{red}{ C}} < 0& to\ the\ right\end{array}
\end{array}
}\)

Answer 11

so the horizontal asymptote is 1