What is a parent function in algebra 2

Table of Contents Show See also[edit] External links[edit] More Specific Topics in Parent Functions and Transformations Popular Tutorials in Parent Functions and Transformations How do you identify parent functions? What is a function in Algebra 2? What are the 4 parent functions?

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In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. For example, for the family of quadratic functions having the general form

the simplest function is

This is therefore the parent function of the family of quadratic equations.

For linear and quadratic functions, the graph of any function can be obtained from the graph of the parent function by simple translations and stretches parallel to the axes. For example, the graph of y = x2 − 4x + 7 can be obtained from the graph of y = x2 by translating +2 units along the X axis and +3 units along Y axis. This is because the equation can also be written as y − 3 = (x − 2)2.

For many trigonometric functions, the parent function is usually a basic sin(x), cos(x), or tan(x). For example, the graph of y = A sin(x) + B cos(x) can be obtained from the graph of y = sin(x) by translating it through an angle α along the positive X axis (where tan(α) = A⁄B), then stretching it parallel to the Y axis using a stretch factor R, where R2 = A2 + B2. This is because A sin(x) + B cos(x) can be written as R sin(x−α) (see List of trigonometric identities).

The concept of parent function is less clear for polynomials of higher power because of the extra turning points, but for the family of n-degree polynomial functions for any given n, the parent function is sometimes taken as xn, or, to simplify further, x2 when n is even and x3 for odd n. Turning points may be established by differentiation to provide more detail of the graph.

See also[edit]

• Curve sketching

External links[edit]

• Video explanation at VirtualNerd.com

More Specific Topics in Parent Functions and Transformations

Popular Tutorials in Parent Functions and Transformations

• How Do You Translate a Function?

  Think about sliding a penny on a table. All you're doing is moving the penny to a new location on the table. That's basically all that's happening when you translate a function! When you translate a function, you're just sliding it to a new location on the coordinate plane!

• How Do You Graph a Translation of a Function?

  A great way to better understand how to translate a function is to practice! This tutorial takes you through the steps of graphing a function that's been translated up and to the right.

• How Do You Reflect a Function?

  When you look in the mirror, you see a reflection of yourself. Reflections in math involve flipping something over a line called the line of reflection. This tutorial shows you how to reflect a function over a chosen line!

• How Do You Graph a Reflection of a Function?

  If you change a function like f(x) to f(-x), it flips the function over the y-axis! Follow along with this tutorial to see how to take a function and reflect it over the y-axis.

• What is a Constant Function?

  Have you ever seen a horizontal line? Then you've seen a constant function! This tutorial introduces constant functions and shows you examples of their equations and graphs!

• What is the Parent Function of a Cubic Function?

  The graph of a linear function is a line. The graph of a quadratic function is a parabola. What does the graph of a cubic function look like? This tutorial introduces you to the basic (parent) function for cubic functions!

• What is a Parent Function?

  Did you know that functions have parents too? Follow along with this tutorial to learn about families of functions and their parent function!

• What is a Cubic Function?

  Cubic functions are just one type of function you’ll see in math. This tutorial introduces you to cubic functions, shows you some examples and graphs, and explains the parent function of cubic functions. Check out this tutorial to learn about cubic functions!

How do you identify parent functions?

What is a function in Algebra 2?

What are the 4 parent functions?