Question

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

Answer 1

Answer:

A. Here the y-intercept is (0,4) and means at time 0 hours the fish is displaced 4 feet.

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

C. The domain is [0, 12].

Step-by-step explanation:

Part A:

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 $m = \frac{y_2-y_1}{x_2-x_1}$. Use the points (0,4) and (1,64).

$m = \frac{y_2-y_1}{x_2-x_1} =\frac{64-4}{1-0} =\frac{60}{1} =60$

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].