Question

a rocket is launched in the air. the graph below shows the height of the rocket h in feet after t seconds. find the interval for which the rocket’s height is increasing.

Explanation:

Step1: Understand Increasing Interval

A function's height (or value) is increasing when, as the input (time \( t \)) increases, the output (height \( h \)) also increases. For a graph, this is the interval where the graph rises from left to right.

Step2: Identify Critical Point

The graph has a peak (vertex) at \( (22, 7744) \). Before this point, the graph is rising (height increasing with time), and after, it's falling (height decreasing with time). The rocket starts at \( t = 0 \) (since it's launched, initial time is 0) and the peak is at \( t = 22 \).

Step3: Determine the Interval

So, the height is increasing when \( t \) is between 0 and 22 seconds, i.e., the interval \( (0, 22) \) (or \( 0 < t < 22 \)).

Answer:

The interval for which the rocket’s height is increasing is \( (0, 22) \) (or \( 0 < t < 22 \) seconds).