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. 

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. 

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. 

This fourth graph is 

The graph
corresponds to this function The new
function is a linear function as two originals. 

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. 

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. 

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. 

The last graph of this pair of
function is 

The new
function is a new linear function. 

Third
Investigation
Well,
now another pair of equation and


The
addition of two linear functions is another linear function. 



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



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



The
function composition is a new linear function. 

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 