Question

A train travels at 100 miles per hour. An equation can be written that compares the time (t) with the distance (d). Define the domain and range.

Answer 1

If t is time and d is distance, and the train travels at 100 mph.

Our equation will look like:

d = 100t, where "t" is in hours

The domain is all possible values of t.  We will assume that negative time isn't a possible thing in this scenario, so the domain of t:

t ≥ 0

The range of this equation is all possible values for d. Since "t" cannot be less than zero, our range:

d ≥ 0

Answer 2

Answer:

Hi!

D(t) = 100t + d₀

where:

t is the time measured in hours.

d₀ is the initial position of the train.

About the domain is t>=0 $\in\Re$.

The range is D(t) $\in\Re$.

Step-by-step explanation:

This equation correspond to a linear function. The general definition of a linear function is:

$f(x)=ax+b$.

where a and b are constants, x is the independent variable and f(x) is the dependent variable.

In addition, we need to define a domain to be a complete function.

The domain are all the values of the independent variable can take.

The range are all the values of the dependent variable can take.

Example:

$Dom(x) \in \Re$

$Range(f(x)) \in \Re$

So the complete form of a linear function with domain and range in Reals is:

$f(x)=ax+b, Dom(x) \in \Re$.