## Precalculus (10th Edition)

The basic function for the given graphs is $y=3^x$. (1) If the function has a horizontal asymptote of $y=a$ and is below the asymptote, it will have the form of: $y=a-3^b$. (2) If the function has a horizontal asymptote of $y=a$ and is above the asymptote, it will have the form of: $y=a+3^b$. (3) The graph of $y=f(x-h)$ involves a horizontal shift of $|h|$ units (to the right when $h \gt 0$, to the left when $h\lt0$) of the parent function $f(x)$. (4) If the graph is increasing, the exponent of $3$ is positive, if it is decreasing, it is negative. (Only if the sign of $3$ is positive, if negative, then if the graph is increasing, the exponent of $3$ is negative, if it is decreasing, it is positive.) The graph in the picture has a horizontal asymptote of $x=0$, is above the horizontal asymptote and increasing. All these are true for A ($y=3^{x})$.