Precalculus: Mathematics for Calculus, 7th Edition

15 1. Start with the parent function $f_1(x)=\cos x$ (Graph:red dashed , amplitude 1, period $2\pi$) If plotting by hand, use Table 2 on page 420 to plot 13 points on $[0,2\pi]$, 2. The graph of $g(x)=3+3f_{1}(x)$ is obtained by vertically stretching by factor 3, (green, dashed) and shifting upwards by 3 units. The new amplitude is 3. Period remains same. Using the table in step 1, multiply each y-coordinate with 3 and add 3. Plot the points $(x, 3+3f_{1}(x))$ and join points with smooth curve (black). =================== Graphing utility used: online calculator desmos.com. The "wrench" button is used to set viewing window settings: radians, step $\pi/4$, ... The accompanying table gives a sufficient number of points for graphing by hand.