20. Let g(t)= cos(31) +2. (a) Write the parent function and draw one cycle here: (b) Find the period. (c) Find the vertical shift. (d) Draw one cycle of the graph. (e) State the domain. (f) State the range.

Use the graphing utility to plot the graphs of y = cos (x) and y = 2x. (Enter multiple functions of x as a comma-separated list.) y = y 3. 2- -4 -3 -2 -1 4 3. 2- 4) 1.

Consider the following function. y = -3.5 cosx + 4) (a) Using pencil and paper, not a graphing utility, determine the amplitude, period, and phase shift for the function. amplitude period phase shift (b) Use a graphing utility to graph the function for two complete cycles. [In choosing an appropriate viewing rectangle, you will need to use the information obtained in part (a).] y y 4 4| 2. -12 \12 я - 12 12 л - 6 -2 2 -4 y y 4 4- 2 2 -3 12 л - 3 12 л - 9 -2 (c) Use the graphing utility to estimate the coordinates of the highest points on the graph. (Round your answers to two decimal places.) (x, y) = (smaller x-value) (x, y) = (| (larger x-value) Use the graphing utility to estimate the coordinates of the lowest points on the graph. (Round your answers to two decimal

Graph f(θ) = sin(πθ) where -2 ≤ θ ≤ 2. State the period of the function.