Question

help im confused...
Amelia is planning the trajectory of her next flight using the altitude and distance from Paris, France. She has determined her function to be f(x) = -4x + 102.

Based on the situation above, describe any necessary restrictions to the domain and range. Provide justification for the restrictions.

Answer 1

@Jaynator495 @dan815 @Compassionate

Answer 2

Domain and range pertain to the restrictions on the values that x and y can be, respectively. The domain of a function depicts all the possible values that x can be, while the range of a function depicts all the possible values that y can be. Thereby, it should be clear that the domain and range are inherently related; one way most look at it is to think that the domain of a function inherently determines the restrictions on the function's range.

An easy way to start to think about it is to look at x and decide what numbers CAN'T be substituted for x. Are there any numbers you can think of that you cannot plug in for x, such that if you do, the function no longer remains a function? Hint: most functions this simple have pretty much no restrictions on the domain, meaning that any value you plug in for x will work.

From there, think of how the function itself is restricted by what you plug in for x. Essentially, now that you've found the possible values of x that the function can adopt, are there any restrictions on the values that f(x) can be? Hint: in most cases, if a function's domain is all-inclusive and has no restrictions, then it is safe to say that the function's range is also all-inclusive and has no restrictions.

Answer 3

Thank you so much. I'm still kinda confused how to go about solving this, but thank you again!