Answer
Please see image for the graphs.
Asymptote of f: $ y=0\quad$(the x-axis)
Work Step by Step
The graph of $f(x)=b^{x}$, when $b\gt 1$, has the following characteristics:
- it is above the x-axis at all times, always rising,
- on the far left, it nears, but never touches the x-axis,
- it rises to cross the y-axis at the point (0,1)
- it rises to pass through the point (1,b),
- and keeps rising...
We use this information to graph $f(x)=2^{x}.$
Calculate f(x) for several values of x:
$$
\left[\begin{array}{ll}
x & f(x)\\
-2 & 1/4\\
-1 & 1/2\\
0 & 1\\
1 & 2\\
2 & 4
\end{array}\right]
$$
and join the points with a smooth curve.
Asymptote of f: $ y=0\quad$(the x-axis)
---
$g(x)=2^{x-1}=f(x-1)$
The graph of $g$ is obtained from the graph of $f $ by shifting it to the right by 1 unit.
The asymptote remains $ y=0\quad$(the x-axis)
