Use a graphing calculator to plot the function's graph. Think about the function. Is a negative altitude possible? How about a negative pressure?
Domain: 0 < P ≤ 30 Range: A(P)≥ 0
Practice makes perfect
To determine a reasonable domain and range for this function, we should start by graphing it.
Graphing the Function
To draw a graph on a calculator, push Y= and type the function in one of the rows. Having written the function, push GRAPH to draw it.
The function is not visible when using a standard window. We can re-size the window by pushing WINDOW and changing the settings. Note that the function's constant is 90 000, which means we have to increase the y-axis to at least 90 000 to capture the graph's behavior when P is small.
Now we can decide what a reasonable domain and range is.
Domain
The function approaches the y-axis asymptotically, which means it is only defined for positive values of P. This makes sense because a negative pressure is not possible. With this information, we can write our lower bound of the range.
P > 0
From the graph, we also see that it intercepts the horizontal axis at 30. Since we cannot have a negative altitude, we have to limit the domain's upper bound to P≤ 30. If we combine the upper and lower bound of the domain, we can write our domain.
0 < P ≤ 30
Range
The range tells us which y-values our function can give. We have already argued that the altitude cannot be zero. With this information, we can write the lower bound of our range.
A(P)≥ 0
Note that the altitude can theoretically go infinitely high, so we are satisfied by keeping a lower bound.
