Question

what are the domain and the range of this relation?
0≤x≤70
x≥0
0≤x≤500
y≥0
0≤y≤500
0≤y≤70

Explanation:

Step1: Determine the domain

The domain of a relation represented by a graph is the set of all possible x - values (input values). Looking at the x - axis (time in minutes), the graph starts at \(x = 0\) and ends at \(x=70\) (since the line touches the x - axis at \(x = 70\)). So the domain is \(0\leq x\leq70\).

Step2: Determine the range

The range of a relation represented by a graph is the set of all possible y - values (output values). Looking at the y - axis (water in gallons), the graph starts at \(y = 500\) (when \(x = 0\)) and goes down to \(y = 0\) (when \(x=70\)). Also, all the y - values between 0 and 500 are covered. So the range is \(0\leq y\leq500\).

Answer:

Domain: \(0\leq x\leq70\)
Range: \(0\leq y\leq500\)