The graph below models the value of a $20,000 car t years after it was purchased.
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A: Each car value, y, is associated with exactly one time, t.***
B: Each time, t, is associated with exactly one car value, y.
C: The rate at which the car decreases in value is not constant.
D: There is no time, t, at which the value of the car is 0.
Please help me, I took my best guess but I need someone to check for me.
I think you want B
y is a function of t.
review what it means to be a function.
A and D are also true, but they are not the reason.
that was not what i was look for but it help me understand so thanks:)
Your answer is correct. Option A is the best statement that describes why the value of the car is a function of the number of years since it was purchased.
In a function, each input, or independent variable, corresponds to exactly one output, or dependent variable. In this case, the number of years since the car was purchased, represented by t, is the input, and the value of the car, represented by y, is the output. Each car value is associated with exactly one time, so option A is the correct choice.
To determine the correct answer, let's break down the options and understand the concept of a function in this context.
A function is a relationship where each input (independent variable) is associated with exactly one output (dependent variable). In this case, the independent variable is the number of years since the car was purchased (t), and the dependent variable is the value of the car (y).
A: Each car value, y, is associated with exactly one time, t.
This statement aligns with the definition of a function. For a specific value of t, there is only one corresponding value of y. Therefore, this option seems correct.
B: Each time, t, is associated with exactly one car value, y.
This statement contradicts the definition of a function. The graph should have only one y-value for each t-value, not the other way around.
C: The rate at which the car decreases in value is not constant.
The constancy or variability of the rate of decrease in car value is independent of the definition of a function. This statement is not relevant to determining if the graph represents a function.
D: There is no time, t, at which the value of the car is 0.
The existence of a time, t, at which the car value reaches zero is also independent of the definition of a function. This statement does not provide information about the association between t and y.
Conclusion:
After analyzing the options, statement A: Each car value, y, is associated with exactly one time, t, aligns with the definition of a function. Therefore, it is the best answer to the question.