Question

Started home. On the way, he stopped at the

library. Then he hurried home. The graph is a
piecewise-defined function that shows Isaac's
distance from home during the time it took him
to arrive home.
3
2.5
2
1.5
1
0.5
0
(0, 3)
(0.5,2)
0.5
1
1.5
(2.5, 2)
2 2.5
3
(3.5, 1.5)
3.5
a. How much time passed between
school ending and Isaac's arrival
home?
b. How long did Isaac stay at Tate's
house?
c. How far is the library from Isaac's
house?
(3.75, 0.01) x
4
4.5
d. Where was Isaac 3 hours after school
ended?
e. Use function notation to write a
mathematical sentence expression
that says the same thing as part d.
f. When was Isaac walking the fastest?
How fast was he walking?

Answer 1

time passed between school ending and Isaac's arrival home can be determined by looking at the x-coordinate values on the graph. From the graph, we can see that Isaac arrived home at the point (3, 0). Since the x-coordinate represents time, we can conclude that Isaac took 3 hours to arrive home after school ended.

b. The length of time Isaac stayed at Tate's house can be determined by finding the difference between the x-coordinate values on the graph. From the graph, we can see that Isaac left the library at the point (2.5, 2) and arrived home at the point (3, 0). Therefore, Isaac stayed at Tate's house for 0.5 hours or 30 minutes.

c. The distance between the library and Isaac's house can be determined by looking at the y-coordinate values on the graph. From the graph, we can see that at the library (2.5, 2), the y-coordinate is 2. This means that the library is 2 units away from Isaac's house.

d. To determine where Isaac was 3 hours after school ended, we can look at the x-coordinate value on the graph. Since Isaac arrived home at the point (3, 0) and we know he took 3 hours to get home, we can conclude that Isaac was still on his way home 3 hours after school ended.

e. In function notation, we can write the same information as part d as: f(3) = 0, where f represents Isaac's distance from home and 3 represents 3 hours after school ended. This means that at 3 hours after school ended, Isaac's distance from home was 0.

f. To determine when Isaac was walking the fastest, we need to look for the steepest slope on the graph. Steeper slopes indicate faster walking speed. From the graph, we can see that the steepest slope occurs between the points (2, 2.5) and (3, 0). This means that Isaac was walking the fastest during the time period from 2 to 3 hours after school ended. The exact speed can be determined by calculating the slope between these two points using the formula: speed = change in distance / change in time.

Explanation: