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Ethan uses the function [tex]f(x) = 2x^2 + 2x + 4[/tex] to track the temperature of a substance over 8 hours. You know that [tex]f(3) = 28[/tex] means that the temperature of the substance is [tex]28^{\circ} C[/tex] when you plug in 3 for [tex]x[/tex].

What is the domain of Ethan's function?

A. The substance
B. The boiling point
C. Temperature
D. Time

Sagot :

GinnyAnsweridn
Let's analyze the given function in the context provided:

Ethan uses the function [tex]\( f(x) = 2x^2 + 2x + 4 \)[/tex] to track the temperature of a substance over time.

The function [tex]\( f(x) \)[/tex] is specifically used to model the temperature of the substance as a function of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] represents time in hours.

In mathematical terms, the domain of a function is the set of all possible input values (in this case, the values of [tex]\( x \)[/tex]) for which the function is defined. Here, [tex]\( x \)[/tex] represents the time over which Ethan is measuring the temperature.

Given that Ethan is tracking the temperature over a period of time (8 hours), the input for the function [tex]\( f(x) \)[/tex] is time. Therefore, the domain of Ethan's function is the set of all possible time values over which he is measuring the temperature.

Thus, the correct answer is:
Time
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