Description: E:\Antillanca\EMAT6680.gif


Rayen Antillanca. Assignment 1


Make up linear function  and . Explore with different pairs of  and  the graph for:

i)              

ii)          

iii)         

iv)          

 

First Investigation

The first pair of functions is:  and  

 

 

This first graph shows

The graph corresponds to this function  

The new function is another linear function.

Description: E:\Antillanca\Assignment1\eq1hi.gif

 

 

This second graph is the multiplication

The graph corresponds to this function

The new function is a quadratic function. The name of the curve is parabola. As the square term is positive, the parabola is concave up.

Description: E:\Antillanca\Assignment1\eq1hii.gif

 

 

The third graph is

The graph corresponds to this function

The new function has an asymptote in the point  because in this point the function is indeterminate; in other words the denominator is zero.

Description: E:\Antillanca\Assignment1\eq1hiii.gif

 

 

This fourth graph is  

The graph corresponds to this function

The new function is a linear function as two originals.

Description: E:\Antillanca\Assignment1\eq1hiv.gif

 

 

Second Investigation

Now, what happen with another pair of functions. The news functions are:  and

 

The first graph is the addition of them, namely

 is the addition of two linear functions the result is another linear function.

Description: E:\Antillanca\Assignment1\eq3hi.gif

 

 

The second graph is the multiplication of them

 

It is the multiplication of two linear functions; the result is a quadratic function. In this case the parabola is concave down because the term square is negative.

Description: E:\Antillanca\Assignment1\eq3hii.gif

 

 

The third graph is the division of them

 is a quotient of two linear equation as result this new function is a hyperbole whose asymptote is when the denominator of the new function is zero.

Description: E:\Antillanca\Assignment1\eq3hiii.gif

 

 

The last graph of this pair of function is

The new function  is a new linear function.

Description: E:\Antillanca\Assignment1\eq3hiv.gif

 

Third Investigation

Well, now another pair of equation  and  

 

The addition of two linear functions is another linear function.

Description: E:\Antillanca\Assignment1\eq5hi.gif

 

 

The product of the functions is a quadratic function, and the parabola is concave down.

Description: E:\Antillanca\Assignment1\eq5hii.gif

 

 

The quotient of two linear equations produce an asymptote when the denominator is zero.

Description: E:\Antillanca\Assignment1\eq5hiii.gif

 

 

The function composition is a new linear function.

Description: E:\Antillanca\Assignment1\eq5hiv.gif

 

 

Summary

When we add 2 linear equations we obtain another linear equation.

When we multiply 2 linear equations we obtain a quadratic function and the graph is a parabola. The parabola is concave up whether the term square is positive, and it is concave down whether the term square is negative.  Is every parabola the result of product of two linear equations?

When we divide 2 linear equation e obtain a hyperbola.

When we take a function as a variable this function is a linear function.

 

 

Note: All graphs of this webpage were made with Graphing Calculator 4.0

 

 

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