Question

1. jetpack: martin flew his new jetpack. he launched from a platform half of a foot above the ground. he flew up into the air and then landed some number of minutes later. use the graph that represents the path of his flight to complete the sentences below.

a. ( a s x
ightarrow-infty, f(x)
ightarrow ) ( a s x
ightarrow infty, f(x)
ightarrow )
b. in the context of the situation being described by the graph, does the end behavior of the graph as ( x
ightarrow infty ) and ( x
ightarrow-infty ) make sense?

Explanation:

Step1: Analyze the end - behavior of the parabola

The graph is a parabola (quadratic function \(y = ax^{2}+bx + c\)). Since the parabola opens upwards (\(a>0\)).
For a quadratic function \(y = ax^{2}+bx + c\) with \(a>0\), as \(x\to-\infty\), \(y = f(x)\to+\infty\) and as \(x\to+\infty\), \(y = f(x)\to+\infty\).

Step2: Consider the context of the jet - pack flight

In the context of Martin's jet - pack flight, \(x\) represents time (in minutes) and \(y\) represents height (in feet). Time \(x\) cannot be negative in this real - world situation. Also, in the real - world, after a certain point (when he lands), the height \(y\) will not increase indefinitely as \(x\) (time) increases.

Answer:

a. As \(x\to-\infty,f(x)\to+\infty\); as \(x\to+\infty,f(x)\to+\infty\)
b. No, the end - behavior of the graph as \(x\to\infty\) and \(x\to-\infty\) does not make sense. Time \(x\) cannot be negative (\(x\to-\infty\) is not relevant for time in this context), and in the real - world, Martin will land (height will not increase indefinitely as \(x\to+\infty\))