www.VirtualNerd.com

What is a Parent Function?

What is a parent function?

Summary

  1. f(x), g(x), h(x), and j(x) are all examples of quadratic functions
  2. The graph of a quadratic function is a parabola
  3. All quadratic functions must have an x2 term as their highest degree term
  4. A group of functions that have similar graphs and equations, like this group here, is called a family of functions
  5. The simplest function in a family of functions is called the parent function
  6. The parent function for all quadratic functions is f(x)=x2

Notes

    1. Some functions are related to each other, just like people in your family are related to you!
    1. These graphs may look slightly different, but they all have the same basic shape
    2. These four functions are a family of graphs
    3. Think about you and your siblings: you all might look similar but you're each slightly different
    4. The same is true in this family of parabolas!
    1. The parent function is the most basic form of the function
    2. All the other functions are just variations on the parent
    1. f(x)=x2 is the parent function for ALL quadratic functions
    2. It is the simplest form of a quadratic function that still counts as a quadratic function
    3. Remember, to be a quadratic a function just needs to have an x2 term as its highest degree term
    4. As long as you still have that x2 term and nothing with a higher degree, you'll still have a quadratic function!
    1. Families of functions are made up of many, many functions, and you might not see all of them listed at once
    2. In fact, the parent function might not always be listed in a family of functions
    3. But it's still just the simplest form of the function that counts as that type of function
    4. For example, the parent function for cubic functions is just f(x)=x3
    1. Here we have a family of linear functions
    2. Notice how each of them has an 'x' term as its highest degree term
    3. All we need in order to have a linear function is an 'x' term with no other higher degree terms
    4. So really all we need is just an 'x'!
    1. Even if h(x)=x wasn't listed here, we could figure out that it was the parent linear function
    2. Since a linear function just needs to have an 'x' term as it's highest degree term, that's all we need for our parent function: an 'x' and nothing else!
    1. All functions in a family of functions can be created by altering the parent function in some way