**☑ Question:** Which of the constants a, b, c and d do you think determine the period, range, x- and y-intercepts in the graph of ? More specifically, what is the period and what is the range? Use this information and try to guess what the graph of would look like.

From our investigation, we found out that |a| affects the range and d results in a vertical shift. Thus, the constants a and d determine the range and the range is .

Also, we found out that |b| affects the period and results in a horizontal shift. Thus, the constants b determines the period. Like we found in our investigation, the period is .

The constants b and c affects the x-intercepts. The y-intercept is equal to asinc+d, thus is affected by a, c, and d.

In the graph of , the original graph of would be compressed vertically, expanded horizontally and shifted to the left and upwards. The range would be and the period would be 4. Let’s check the graph: