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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|
  • Quadratic Functions
    • 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

Alg2A 4.3 Parent Functions

  • Parent Function Rules

Alg2A 4.3 Parent Functions Chart

  • Other Important Parent Functions

alg2b 4.3 exponential fx alg2b 4.3 sq rt fx alg2b 4.3 log fx

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