Answer
domain: $(-\infty,\infty)$
range: $(0,\infty)$
asymptote: $ y=0$
Work Step by Step
The graph of $ f(x)=2^{x}$ is
- always above the x-axis, - the x-axis ( $ y=0$ ) is the asymptote.
- from left to right, always rises and passes through $(-1,\displaystyle \frac{1}{2}),\ (0,1),\ (1,2)$, and $(2,4)$.
Plot these points and join with smooth curve (black, dashed line).
$ g(x)=\displaystyle \frac{1}{2}\cdot 2^{x}=2\cdot f(x)$, so its graph is obtained by
vertically compressing the graph of $ f(x)$ by a factor $\displaystyle \frac{1}{2}$ (the asymptote remains $ y=0$ )
Perform the transformation on the four points found above, and join the new points with a smooth curve (red, solid line).
domain: $(-\infty,\infty)$
range: $(0,\infty)$
asymptote: $ y=0$
