Precalculus Function and Graph

Precalculus is one of the most important and interesting branch of mathematics.
Functions are basically the mappings by which elements of a given set are uniquely related to the elements of the other set. Each element on the domain have a unique image onto its co domain.
Graphs are the representation of functions on to the 2-d space . It desribes the nature of the functions . Graph can be possibly different for various classes of functions .

In this article we are going to deal with the functions and its graphs.

Precalculus Function and Graph : Examples

Example 1  : Make the graph for the precalculus function y = `e^x`

Solution : 

The `e^x` is the exponentail function . The domain is the set of all the real numbers while the range is the set of all positive real numbers.

For making the graph , we have to find the plotting points.

By putting x = 0 in the given equation , we get

y = `e^0`   =  1

By putting x = 1 in the given equation , we get

y= `e^ 1` = e = 2.71

By putting x = 0 in the given equation , we get

y = `e^2` =  7.38

x	0	1	2	3
f(x)	1	2.71	7.38	20.08

Graph is as shown :

            

Example 2  : Make the graph for the precalculus function y = ln x

Solution : 

The ln x is the natural logarithmic  function . The domain is the set of all the positive real numbers while the range is the set of all real numbers.

For making the graph , we have to find the plotting points.

By putting x = 1 in the given equation , we get

y = ln (1)   =  0

By putting x = 2 in the given equation , we get

y = ln (2)  = 0.69

By putting x = 3 in the given equation , we get

y = ln (3) = 1.09

x	0.5	1	2	3
f(x)	-0.69	0	0.69	1.09

Graph is as shown :

            

Precalculus Function and Graph : Practice Problems

Problem 1  : Make the graph for the precalculus function y = `|x|`

Problem 2  : Make the graph for the precalculus function y = sgn (x)