Question

the density of a gas under constant pressure depends on temperature. holding pressure constant at 14.5 pounds per square inch, a chemist measures the density of a sample of an element at temperatures 0, 27, 60, 80, and 115°c and obtains densities of 1.464, 1.274, 1.201, 1.101, and 1.016 kg/m³, respectively. (a) what is the domain and range of the relation? (b) express the relation using a mapping. (c) express the relation as a set of ordered pairs. (a) the domain of the relation is and the range is (use a comma to separate answers as needed.)

Explanation:

Step1: Identify domain

The domain is the set of input values, which here are the temperatures. So the domain is $\{0, 27, 60, 80, 115\}$.

Step2: Identify range

The range is the set of output values, which are the densities. So the range is $\{1.464, 1.274, 1.201, 1.101, 1.016\}$.

Step3: Express relation as mapping

We map each temperature to its corresponding density. For example, $0
ightarrow1.464$, $27
ightarrow1.274$, $60
ightarrow1.201$, $80
ightarrow1.101$, $115
ightarrow1.016$.

Step4: Express relation as ordered - pairs

An ordered pair is of the form (input, output). So the set of ordered pairs is $\{(0,1.464),(27,1.274),(60,1.201),(80,1.101),(115,1.016)\}$.

Answer:

(a) Domain: $0, 27, 60, 80, 115$; Range: $1.464, 1.274, 1.201, 1.101, 1.016$
(b) $0
ightarrow1.464$, $27
ightarrow1.274$, $60
ightarrow1.201$, $80
ightarrow1.101$, $115
ightarrow1.016$
(c) $\{(0,1.464),(27,1.274),(60,1.201),(80,1.101),(115,1.016)\}$