# EXPLORING PROPERTIES OF PARENT FUNCTIONS

## About "Exploring properties of parent functions"

Exploring properties of parent functions :

In mathematics, every function can be classified as a member of a family. Each member of a family of functions is related to the simplest, or most basic, function sharing the same characteristics.This function is called the parent function.

Exploring the properties of parent functions is trying to know something about it like its graph, name, its family members etc.,

## Exploring properties of parent functions

Now, let us look at some different parent functions, their family name, family members and examples.

Family : Linear functions

Parent function : f(x)  =  x

Family members : f(x)  =  mx + b

Examples : f(x)  =  3x + 2, f(x) = -3x + 4

Special features :

(i)  Straight line goes through the origin

(ii)  Slope is 1

(iii)  Divides the plane exactly in half diagonally

(iv)  Graph only quadrants 1 and 3

Graph of the parent function f(x) = x :

Parent function : f(x)  =  x²

Family members : f(x)  =  a(x - h)² + k

Examples : f(x)  =  5(x - 3)² - 2 , f(x) = -x² + 3

Special features :

(i)  Parabola that opens up ward

(ii)  Vertex at the origin

(iii)  y has a minimum value

(iv)  y-axis is axis of symmetry

(v)  Graph only in quadrants 1 and 2

Graph of the parent function f(x) = x² :

Family : Square root functions

Parent function : f(x)  =  x

Family members : f(x)  =  a (x - h) + k

Examples : f(x)  =  5 (x - 3) - 2, f(x)  =  -  x + 3

Special features :

(i)  Semi parabola that opens right ward

(ii)  Vertex at the origin

(iii)  x has a minimum value

(iv)  x-axis is axis of symmetry

(v)  Graph only in quadrant 1

Graph of the parent function f(x) = x :

Family : Reciprocal function or Rational function

Parent function : f(x)  =  1/x

Examples : f(x)  =  1/(x - 3), f(x)  =  2/(3x + 5)

Special features :

(i)  This curve has two parts

(ii)  Horizontal asymptote is y = 0

(iii)  Vertical asymptote is x = 0

(v)  Graph only quadrants 1 and 3

Graph of the parent function f(x) = 1/x :

Family : Absolute value function

Parent function : f(x)  =  |x|

Examples : f(x)  =  2|x+3|, f(x)  = |x| + 5

Special features :

(i)  V-shaped curve and open upward

(ii)  Vertex at the origin

(iii)  y has a minimum value

(iv)  y-axis is axis of symmetry

(v)  Graph only quadrants 1 and 2

Graph of the parent function f(x) = |x| :

After having gone through the stuff given above, we hope that the students would have understood "Exploring properties of parent functions".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6