Question

In the following​ situation, state whether two variables are related in a way that might be described by a function. If​ so, identify the independent and dependent variables. You jump from an airplane (with a parachute )jump from an airplane (with a parachute) and want to know how far you have traveledwant to know how far you have traveled at various times during your descent.at various times during your descent. nothing Determine whether the two variables are related in a way that might be described by a function. If the situation could be described as a​ function, then identify the independent and dependent variables. Choose the correct answer below.

Answer 1

Answer:

The situation CAN be described as a function.

The independent variable is the time t that have passed since you jumped from the plane.

The dependent variable is the distance d you have traveled since you jumped from the plane.

Step-by-step explanation:

A function f is a relation between 2 sets A and B that assigns only one element y of B to each element x (called independent variable) in a certain subset of A (that could be A itself). In this case we write  

$f:A\rightarrow B$

$f(x)=y$

and we say x is the independent variable and y is the dependent variable.

The key words here are “only one element y of B”.

That means that for example, a relation between integers such that f(1)=2 and f(1)=3 cannot be a function.

The case described in this problem could be described as a function

$\bf {f:\mathbb{R}^+\rightarrow \mathbb{R}^+$

$f(t)=d}$

where $\mathbb{R}^+$ is the set of positive real numbers, t is the time that have passed since you jumped from the plane and d the distance you have traveled since you jumped from the plane.

Since that at a given time you have only traveled one distance, this is actually a function.

In this case, the independent variable is the time t that have passed since you jumped from the plane, and the dependent variable is the distance d you have traveled since you jumped from the plane.