Question

3.
a ball bounces several times after it is
dropped. the graph shows the height of
the ball over time.
height is measured in meters and time is
measured in seconds.

select all statements that are true about the graph and the situation it represents.
a. the vertical intercept shows the time when the ball hits the ground.
b. the vertical intercept shows when the ball is dropped.
c. the function reaches its maximum value after the first bounce.
d. the function has the maximum value at the vertical intercept.
e. the horizontal intercepts of the graph show the times when the ball hit the
ground.
f. the function has no minimum value.
g. there are multiple times when the function is at its minimum value.

4.
function $r$ gives the amount of rain measured by a rain gauge $t$ hours since it started
raining. the amount of rain is measured in millimeters.

a. what does each expression or equation represent in this situation?
i. $r(3)$
ii. $r(0.5)=14$

b. use function notation to represent each statement.
i. six hours after it started raining, the amount of rain was 37 millimeters.
ii. the amount of rain 90 minutes after it started raining was the same as the
amount 120 minutes after it started raining.

Explanation:

Problem 3

• A: Vertical intercept is at \(t=0\), height=2m (drop height), not ground hit time. False.
• B: Vertical intercept (\(t=0\)) is when the ball is dropped. True.
• C: The maximum height is at \(t=0\), not after first bounce. False.
• D: The highest point (max value) is the vertical intercept (\(h=2\) m). True.
• E: Horizontal intercepts are where \(h=0\), meaning the ball hits the ground. True.
• F: The function has a minimum value of 0 (when the ball hits the ground). False.
• G: The ball hits the ground multiple times, so the function is at minimum (0) multiple times. True.

Part a

i. \(R(t)\) is rain in mm at \(t\) hours after rain starts. \(R(3)\) is the rain amount at 3 hours.
ii. \(R(0.5)=14\) means at 0.5 hours (30 mins) after rain starts, rain is 14 mm.

Part b

i. 6 hours after start, rain is 37 mm: use \(R(6)\) for the amount at 6 hours.
ii. 90 minutes = 1.5 hours, 120 minutes = 2 hours. Equal rain amounts mean \(R(1.5)=R(2)\).

Answer:

B. The vertical intercept shows when the ball is dropped.
D. The function has the maximum value at the vertical intercept.
E. The horizontal intercepts of the graph show the times when the ball hit the ground.
G. There are multiple times when the function is at its minimum value.

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Problem 4