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If all the variables in a function change, why are some variables called independent and other variables called dependent?

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Because the dependent variable DEPENDS on the independent. Let me explain further by an example: Say you want to understand the relationship between people's wealth (how much money they have) and age. You might have a graph that looks like this:
You have the x-axis as the independent variable and the y-axis as the dependent variable. You FIX the age (you ask people what their age is), and DEPENDING on what their age is, they will have a different answer for their wealth. And it makes sense that your wealth could depend on age since as you get older, you work more (earn more money). In the graph you see a decline at age 60 because now that person might be retired and not earning a salary like before

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Other answers:

kirbykirby's response is good. @pinkgrapefruit is that a ragdoll cat in your profile picture?
So basically "dependent" and "independent" just tell you HOW the variables relate to each other, but they are still changing in value (so they are still "variables")
thank you! and i'm really sorry if this is a stupid question but basically however the dependent variable changes that doesn't affect the independent variable right? like the money depends on the age but the age doesn't depend on the money and yes @agent0smith it is :)
Here's an example. Let's say you drive a car and you get gas. Gas costs $3.50 per gallon. The gas pump calculates how much you need to pay. You choose how many gallons you buy. The number of gallons you get is the independent variable. It is completely arbitrary and is completely up to you. You may buy 5 gallons one day, 8 gallons another day, 3 gallons on another day, but once the number of gallons is fixed, you have no choice on the total cost. The day you get 5 gallons, you pay $3.50 x 5 = $17.50. That day you get 8 gallons, you pay $3.50 x 8 = $28, and the day you get 3 gallons, you pay $3.50. The cost is the dependent variable. It depends on what the independent varaible was and the relation between them. The cost can be given by the relation c = 3.5g (cost = 3.5 x (number of gallons).
^ Yes I would say that is a better example than mine because there is an actual mathematical relationship between x and y. Mine is more like a "correlation" (I am thinking too much about stats loool)
It's more clear to understand the dependence/indeoendence in @mathstudent55's example
And yes you're right about this: like the money depends on the age but the age doesn't depend on the money In general: y depends on x, but x doesn't depend on y
oh ok thank you i get it now! thank you for both of the examples this really helped me a lot :)
You're welcome.
Your welcome :) And it's not a stupid question. I was confused about the same thing when I first started learning about it, and now I'm majoring in math in university ;) So don't give up!!

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