Question

The table below represents the displacement of a duck from its nest as a function of time.
time(x) displacement(y)
0 7
1 29
2 51
3 73
4 95
Part A: What is the y-intercept of the function and what does this tell you about the duck? (4 points)
Part B: Calculate the average rate of change of the function represented by the table between x=2 to x=4 hours? (4 points)
Part C: What would be the domain of the function if the duck continued to walk at this rate until it traveled 227 miles from the

Answer 1

Part A: What is the y-intercept?
What does this tell you about the duck?
Part B: What is the average rate of change from x = 2 to x = 4? Show your work.
Part C: Write a compound inequality of the domain if he traveled 227 miles from the nest?

Answer 2

@aum @perl

Answer 3

y-intercept is the y-value when x = 0.
From the table, what is the y-value when x = 0?

Answer 4

7

Answer 5

Correct. y-intercept = 7
What does this tell you about the duck? At time x = 0, the duck is 7 units away from the nest. That means the duck was NOT in its nest at time x = 0.

Answer 6

Part B: What is the average rate of change from x = 2 to x = 4? Show your work.

Average rate of change = \(\Large \frac{y_2-y_1}{x_2-x_1}\)

Read the y-values from the table when x = 2 and when x = 4

Average rate of change = \( \Large \frac{95-51}{4-2} = ?\)

Answer 7

44/2

Answer 8

@aum

Answer 9

44 / 2 = 22.

Part B: What is the average rate of change from x = 2 to x = 4? 22
Show your work: See previous reply

Answer 10

C) Slope = 22 (same as average rate of change found in part B.)
y = mx + b
y = 22x + b
when x = 0, y = 0 + b
y = b
From the table, when x = 0, y = 7.
Therefore, b = 7

y = 22x + 7

Part C: Write a compound inequality of the domain if he traveled 227 miles from the nest?
Set y = 227 in y = 22x + 7
227 = 22x + 7
227 - 7 = 22x
22x = 220
x = 10

Domain is x = 0 to x = 10. Or, domain is: [0, 10].

Answer 11

Compound inequality for the domain: \(\large 0 \le x \le 10\)