Question

1. match each feature of the situation with a corresponding statement in function notation.

a. maximum height 1. $h(0) = 7$
b. minimum height 2. $h(1.5)$
c. height staying the same 3. $h(4)$
d. starting height 4. $h(t) = 6$ for $7 \leq t \leq 8$

Explanation:

Step1: Analyze Option A (Maximum Height)

The graph of height vs. time shows the peak (maximum height) at \( t = 4 \) seconds. So the function value at \( t = 4 \), i.e., \( h(4) \), represents the maximum height.

Step2: Analyze Option B (Minimum Height)

The graph has a minimum (lowest point) around \( t = 1.5 \) seconds. Thus, \( h(1.5) \) gives the minimum height.

Step3: Analyze Option C (Height Staying Same)

For \( 7 \leq t \leq 8 \), the graph is horizontal, meaning height is constant. The statement \( h(t) = 6 \) for \( 7 \leq t \leq 8 \) describes this constant height.

Step4: Analyze Option D (Starting Height)

The "starting height" is at \( t = 0 \) (initial time). From the graph, \( h(0) = 7 \), so this matches the starting height.

Answer:

A. maximum height - 3. \( h(4) \)
B. minimum height - 2. \( h(1.5) \)
C. height staying the same - 4. \( h(t) = 6 \) for \( 7 \leq t \leq 8 \)
D. starting height - 1. \( h(0) = 7 \)