Answer
Please see image for the graphs
Asymptote of f: $ y=0\quad $(the x-axis)
Asymptote of g: $ y=1$
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)=3^{x}.$
Calculate f(x) for several values of x, and plot the points $(x,f(x)$.
Join the points with a smooth curve.
Asymptote of f: $ y=0\quad $(the x-axis)
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$ g(x)=3^{x}+1=f(x)+1$
The graph of $ g $ is obtained from the graph of $ f $ by
raising it upwards by 1 unit.
The asymptote also rises to $ y=1.$
