Question

2.3.3 quiz: graphs of functions
a. after 40 minutes, sam is 40 meters from the dock.
b. after 3 minutes, sam is 3 meters from the dock.
c. after 3 minutes, sam is 40 meters from the dock.
d. after 40 minutes, sam is 3 meters from the dock.

Explanation:

Step1: Analyze the graph's slope and intercept

The graph has a y - intercept of 20 (when \(x = 0\), \(y=20\)) and we can find the slope. Let's take two points, say \((0,20)\) and \((11,100)\). The slope \(m=\frac{100 - 20}{11-0}=\frac{80}{11}\approx7.27\). The equation of the line is \(y = 20+\frac{80}{11}x\).

Step2: Evaluate each option

• Option A: When \(x = 40\), \(y=20+\frac{80}{11}\times40=20+\frac{3200}{11}\approx20 + 290.91=310.91

eq40\). So A is wrong.

• Option B: When \(x = 3\), \(y=20+\frac{80}{11}\times3=20+\frac{240}{11}\approx20 + 21.82 = 41.82\approx40\) (close enough due to slope approximation, but more accurately, let's check the graph scale. Wait, maybe the x - axis is misread? Wait, the x - axis is labeled "Times (minutes)" with ticks at 0,1,2,3,4,5,6,7,8,9,10,11. Wait, maybe the options have a typo? Wait, no, maybe I misread the options. Wait, option C says "After 3 minutes, Sam is 40 meters from the dock". Let's recalculate with the correct slope. Wait, the line goes from (0,20) to (11,100). The change in y over 11 minutes is 80 meters. So per minute, about \(\frac{80}{11}\) meters. At \(x = 3\), the distance is \(20+3\times\frac{80}{11}=20+\frac{240}{11}=\frac{220 + 240}{11}=\frac{460}{11}\approx41.8\), which is close to 40? Wait, maybe the x - axis is actually 0 - 10 minutes? Wait, no, the graph's x - axis has ticks up to 11. Wait, maybe the options have a mistake, but among the options, when we check the values:
• Option C: After 3 minutes, let's see the graph. At x = 3, the y - value (distance) is around 40 (since from (0,20) to (11,100), at x = 3, the line is at y=20 + (80/11)*3≈41.8, which is close to 40, and the other options are way off. Option B says 3 meters, which is wrong. Option D: At x = 40, y is not 3. So the best option is C.

Answer:

C. After 3 minutes, Sam is 40 meters from the dock.