what is the definition of a parent function?

Hey there!

To start, we can learn about families of functions. Examples of this would include linear and quadratic functions. In these "families", or groups of functions, we have one function that's the most simple, and that all other functions in the family are based upon. For example, in quadratics, the parent function is:

f(x) = x^2

However, that's only the simple, basic, parabola with one solution. We can add on to that, make it more narrow, move it up and down, left and right, and even make it wider by adding, subtracting, and multiplying numbers to that parent function. For example,

f(x) = 2x^2

would make it narrower. For linear functions, it's the same, but with a different parent function:

y = x

If we add, subtract, multiply, or divide, we can change things like the slope and y-intercept.

Hope this helps!