Some Standard Function-I

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Here are some functions we will encounter frequently. Note carefully their domains and Ranges and remember the graph and carefully observe how they have been plotted

A. For finding the domain use VERTICAL LINE TEST(previous post click here )

B. For finding the Range use 'HORIZONTAL LINE TEST'

 1. Constant function f(x) = k

 Domain = R

 Range = {k}

2. Identity function 
f(x) = x

 Domain = R

 Range = R



 3. Linear function f(x) = mx + c
Domain = R
Range = R



4. Square or quadratic function  f(x) = {x^2}

 Domain = R

 Range = [0,\infty )

For, x = a or x = - a ,  f(x) = {a^2},means graph of positive side of x - axis and graph of negative side of x-axis are same.
5. Cube Function f(x) = {x^3}

 Domain = R

 Range = R

if x = a, f(x) = {a^3} and if x = - a, f(x) = - {a^3} , 
i.e. graph of f(x) = {x^3} is below the x-axis for x < 0, and above the x-axis for x > 0



 6. Reciprocal function f(x) = \frac{1}{x}
( since {\rm{denominator}} \ne {\rm{0}})

 Since,
 Range: The possible point of y for which we can get finite value of x 
y = \frac{1}{x} \Rightarrow x = \frac{1}{y} , 

Thus, Domain and Range never get the value 'zero'.

 Domain = R - {0}

 Range = R - {0}


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