# 4.3 – Parent Functions

## Objectives

• Define parent function.
• List the key properties of and identify the graph of the linear parent function.
• List the key properties of and identify the graph of the quadratic parent function.
• List the key properties of and identify the graph of the absolute value parent function.
• List the key properties of and identify the graph of the reciprocal parent function.
• Identify the parent function when you are given a list of functions.

## Key Terms

• Absolute Value – A numbers distance from zero on a number line.
• Absolute Value Parent Function – The function F(x) = |x|.
• It is the most basic function of the absolute value family of functions, and it is used as a building block for more complicated functions.
• Linear Parent Function – The function F(x) = x.
• It is the most basic function of the linear family of functions, and it is used as a building block for more complicated functions.
• Parent Function – A basic function that is used as a building block for more complicated functions.
• Quadratic Parent Function – The function $F(x)=x^2$.
• It is the most basic function of the quadratic family of functions, and is used as a building block for more complicated functions.
• Reciprocal – One of two numbers whose product is 1. If x is not equal to 0, then the reciprocal of x equals $\frac{1}{x}$ .
• You can find the reciprocal of a fraction by switching the numerator and denominator.
• Reciprocal Parent Function – The function $F(x)=\frac{1}{x}$ .
• It is the most basic function of the reciprocal family of functions, and is used as a building block for more complicated functions.

## Notes

Parent Functions
• In each family of functions, the parent function is the most basic function in the family.
• Linear Functions
• Straight lines
• They go through the origin
• They have a slope of 1
• They exist only in quadrants I and III
• Written Form: F(x) = x
• Also seen written as a linear equation: y = x
• Absolute Value Functions
• It is in quadrants I and II
• It is V-shaped
• It goes through the origin
• The left half has a slope of -1
• The right half has a slope of 1
• Written Form: F(x) = |x|
• They go through the origin
• They exist only in quadrants I and II
• They are parabolas
• Written Form: $F(x)=x^2$
• Also seen written as a parabolic equation: $y=x^2$
• Reciprocal Functions
• They do NOT go through the origin
• They are always in quadrants I and III
• They are hyperbolas
• Written Form: $F(x)=\frac{1}{x}$
• Graphs of Parent Functions

• Parent Function Rules

• Other Important Parent Functions