## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Domain: $\mathbb{R}$. Range: $(0,\infty)$ Graph: The graph of this function is obtained from $f_{1}(x)=e^{x}$, by shifting it to the left by 2 units (subtract 2 from each x-coordinate) Graph, with a dashed line, the graph of $f_{1}(x)=e^{x}$, as instructed in the solution of exercise 47$:$ ...Graphing $f_{1}(x)=e^{x}$ , ... The base is $e\approx 2.718\gt 1$, so the graph rises on the whole domain. ... Asymptote is the x-axis. ... To the far left, the graph nears but does not cross the asymptote. ... The graph passes through the points ... $(-1,\displaystyle \frac{1}{e}),(0,1),(1,e),(2,e^{2})$, and so on. ... Plot these points and join with a smooth curve. Then, for each of the points used for graphing $f_{1}$ perform the above transformations (subtract 2 from each x-coordinate) plot the new points, and join with a smooth curve (red on the image). The asymptote remains the x-axis. Domain: $\mathbb{R}$. Range: $(0,\infty)$