How to find attributes from a function in machine learning?

Question

I have started learning machine learning. I have a question in mind. Is it possible to know how many attributes or features a certain model has by seeing its equation? Suppose a function given below:

$$f(x) = 2.54 x^2 + a x + 3.10 $$ How many attributes or features does this model have in machine learning?

Answer 1

You can look at it from two different perspectives

Non-linear model

In this case, there's only one feature $x$

Linear model

If you call $z_0 = x^0 = 1$, $z_1=x^1$, $z_2 = x^2$ then your model becomes

$$ g(z_0,z_1, z_2) = 2.54z_2 + a z_1 + 3.10 z_0 $$

which is a linear model with three features: $z_0, z_1$ and $z_2$