College Algebra, Chapter 3, 3.5, Section 3.5, Problem 64

Graph the functions on the same screen with viewing rectangle $[-5,5]$ by $[-4, 4]$

How are the graphs related to each other?

a.) $y = f(x) = \sqrt{2x - x^2}$

b.) $y = f(-x)$

c.) $y = - f(-x)$

d.) $y = f(-2x)$

e.) $\displaystyle y = f \left( \frac{-1}{2}x \right) $







The graph of $y = f(-x)$ is obtained by reflecting the graph of $y = f(x)$ about $y$-axis. Then, the graph of $y = -f(-x)$ is obtained by reflecting the graph of $y = f(-x)$ about $x$-axis. Then, the graph of $y = f(-2x)$ is obtained by reflecting the graph of $y = f(x)$ about $y$-axis then the result is shrunk horizontally by a factor of $\displaystyle \frac{1}{2}$. Lastly, the graph of $\displaystyle y = f \left( \frac{-1}{2} x \right)$ is obtained by reflecting the graph if $y = f(x)$ about $y$-axis then the result is stretched horizontally by a factor $\displaystyle \frac{1}{2}$.