College Algebra, Chapter 3, 3.5, Section 3.5, Problem 62

Graph the functions on the same screen with viewing rectangle $[-6,6]$ by $[-4, 4]$

How are the graphs related to each other?

a.) $\displaystyle y = \frac{1}{\sqrt{x}}$

b.) $\displaystyle y = \frac{1}{\sqrt{x + 3}}$

c.) $\displaystyle y = \frac{1}{2 \sqrt{x + 3}}$

d.) $\displaystyle y = \frac{1}{2 \sqrt{x + 3}} - 3$







The graph of $\displaystyle y = \frac{1}{\sqrt{x + 3}}$ is obtained by shifting the graph of $\displaystyle y = \frac{1}{\sqrt{x}}$ three units to the left. Then, the graph of $\displaystyle y = \frac{1}{2 \sqrt{x + 3}}$ is obtained by shrinking the graph of $\displaystyle y = \frac{1}{\sqrt{x + 3}}$ vertically by a factor of 2. Lastly, the graph of $\displaystyle y = \frac{1}{2 \sqrt{x + 3}} - 3$ is obtained by shifting the graph of $\displaystyle y = \frac{1}{2 \sqrt{x + 3}}$ three units downward.