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