13. communicate and justify during a chemistry experiment, julian records how the temperature changes over time using ordered pairs (time in minutes, temperature in °c). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) a. which variable is the independent variable? the dependent variable? explain. b. is the relation a function? explain. c. which variable represents the input of the relation? the output? d. what are the domain and range of this relation?

Question

Accepted Answer

### Part a
# Brief Explanations:
In an experiment, the independent variable is the one that is manipulated or controlled (time here, as it's set by the experimenter), and the dependent variable depends on it (temperature, as it changes with time).
# Answer:
Independent variable: Time (in minutes) because it is the variable that is controlled or changed in the experiment. Dependent variable: Temperature (in $^\circ\text{C}$) because it depends on the time elapsed during the experiment.

### Part b
# Brief Explanations:
A relation is a function if each input (time value here) has exactly one output (temperature value). Checking the ordered pairs, each time (first element of the pair) is unique or maps to only one temperature.
# Answer:
Yes, the relation is a function. Because for each input value of time (the first element in each ordered pair), there is exactly one corresponding output value of temperature (the second element in each ordered pair). None of the time values (inputs) are repeated with different temperature values (outputs).

### Part c
# Brief Explanations:
In a relation, the input is the independent variable (time, as it's the first element in ordered pairs) and the output is the dependent variable (temperature, the second element).
# Answer:
Input: Time (in minutes) (since it is the independent variable and the first component of the ordered pairs). Output: Temperature (in $^\circ\text{C}$) (since it is the dependent variable and the second component of the ordered pairs).

### Part d
# Explanation:
## Step1: Find the domain
The domain of a relation is the set of all input values (time values here). From the ordered pairs $(0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100)$, the time values (first elements) are $0, 5, 10, 15, 20, 25$. So the domain is the set of these values.
## Step2: Find the range
The range of a relation is the set of all output values (temperature values here). From the ordered pairs, the temperature values (second elements) are $15, 20, 50, 80, 100, 100$. Removing duplicates, we get $15, 20, 50, 80, 100$.
# Answer:
Domain: $\{0, 5, 10, 15, 20, 25\}$ (set of all time values). Range: $\{15, 20, 50, 80, 100\}$ (set of all temperature values, with duplicates removed).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part a

Answer:

Part b