Your high schooler’s stumbling block just seems to be the notation?
Taking a step back, to motivate the notation, we can start with simple intuitive examples. Suppose I mail people twice as much money as they mail to me. You mail me $2, I mail you back $4. If you mail me $2.50, I mail you back $5.
You can send any amount, so let’s use a placeholder *x* to represent the amount.
My job is to double that amount, which can now be expressed as 2*x*.
That’s my job. That’s my “function”, here. Right? My “function” is to receive *x*, and return 2*x*. That’s one way to help remember the terminology.
“My function expects me to receive *x* from you” can be written in math notation as *f*(*x*) . It’s like a drawing of me holding *x* in my arms.
And what do I return to you? In my example, we said it’s 2*x*.
So, in full math notation, we can write this example as *f*(*x*) = 2*x*
That’s one relation. All kinds of relations can be expressed through functions, including trigonometric relations and more.
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