Question

a plant is 2 inches tall. in sunlight, the plant grows 1 inch each week. at the end of the 4th week, the plant is placed in a dark room for 2 weeks and stops growing. it is then returned to the sunlight and grows at the same rate for the next 3 weeks. describe how you would go about sketching the graph of this relationship. include key features of the graph in your description.

Explanation:

1. First, identify the initial - height: The plant starts at a height of 2 inches, so the y - intercept of the graph (when x = 0, where x is the number of weeks) is 2.
2. Analyze the growth phase 1: For the first 4 weeks, it grows 1 inch per week. The slope of the line for this part (0 ≤ x ≤ 4) is 1. We can use the point - slope form y=mx + b (where m = 1 and b = 2) to find the height at x = 4, which is y=1×4 + 2=6 inches.
3. Analyze the non - growth phase: For the next 2 weeks (4 < x ≤ 6), the plant's height remains constant at 6 inches. So, this part of the graph is a horizontal line at y = 6.
4. Analyze the growth phase 2: For the next 3 weeks (6 < x ≤ 9), it resumes growing at a rate of 1 inch per week. We start from the point (6, 6) and with a slope of 1. We can find the height at x = 9 using the point - slope form y - y1=m(x - x1), where (x1,y1)=(6,6) and m = 1. So y=1×(9 - 6)+6=9 inches.

Answer:

First, mark the point (0, 2) on the graph as the initial height. Draw a line with a slope of 1 from x = 0 to x = 4. At x = 4, the height is 6 inches. Then draw a horizontal line from x = 4 to x = 6 at y = 6. After that, starting from the point (6, 6), draw a line with a slope of 1 from x = 6 to x = 9. The key features are the y - intercept at (0, 2), slopes of 1 for the growing periods, and a horizontal line for the non - growing period.