Question

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)

Answer 1

Part A

To find the y-intercept, put x=0 and find for y;

As you can see from the the table when x=0 , y=4 this means, that the fish started off 4 feet away from its reef

At 0 hours, the distance it's away from its reef is, 4 feet

Part B

The average rate of change of the function calculates the slope of the line or a curve on a given range.

The average rate of the change of function represented by the table between x=1 to x=3 hours is 60.

The average rate represents the speed of the fish in feet\ hour.

Part C:

To find the domain of the function :

Now, we know the slope and the y-intercept. We can easily find the equation of the line y=mx+b where m is the slope and b is the y-intercept. if the fish continued to swim at this rate until it traveled 724 feet from the reef.

724=60x+4

724-4=60x

→ 60x=720

On simplify we get;

x=12

The fish would take 12 hours to travel 724 feet from the reef.

so, the domain of the function would be between 0 and 12.

Answer 2

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

To find the y-intercept, put x=0 and find for y;

As you can see from the the table when x=0 , y=4 this means, that the fish started off 4 feet away from its reef

At 0 hours, the distance its away from its reef is, 4 feet

Part B

The average rate of change of the function calculates the slope of the line or a curve on a given range.

For any point the slope between the ordered pairs (1, 64) and (3, 184).

the formula of slope is given by:

Slope
`=(y_(2)-y_(1))/(x_(2)-x_(1))`
`=(184-64)/(3-1) =(120)/(2) =60`

The average rate of the change of function represented by the table between x=1 to x=3 hours is, 60.

The average rate represents the speed of the fish in feet\ hour.

Part C:

To find the domain of the function :

Now, we know the slope and the y-intercept we can easily find the equation of the line
`y =mx+b` where m is the slope and b is the y-intercept.

∵ m =60 and b=4, we have
`y=60\cdot x+ 4`,

if the fish continued to swim at this rate until it traveled 724 feet from the reef.

`724=60x+4`

`724-4=60x`

⇒
`60x=720`

On simplify we get;

`x=12`

∴the fish would take 12 hours to traveled 724 feet from the reef.

so, the domain of the function would be between 0 and 12.