The table below represents the displacement of a fish from its reef as a function of time:

Time
(hours)
x Displacement
from reef
(feet)
y
0 4
1 64
2 124
3 184
4 244

Part A: What is the y-intercept of the function, and what does this tell you about the fish? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points)

Part C: What would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

The y-intercept is where the function intersects the y-axis. It is the point (0,b) and is always the starting value in real world situations since time begins at x=0. Here the y-intercept is (0,4) and means at time 0 hours the fish is displaced 4 feet.

Part B:

The average rate of change is the slope of the function found using the formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Use the points (0,4) and (1,64).

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{64-4}{1-0} =\frac{60}{1} =60[/tex]

For every hour, the fish is displaced 60 more feet.

Part C:

The domain is the set or group of x values in the function. Time starts at 0 and goes until the fish traveled 724 feet. What time is this at?

The function has the equation y = 60 +4. Find the time by substituting y=724.

724=60x+4

720 = 60x

12=x.

The domain is [0, 12].