Solve Horizontal Line Test

HORIZONTAL LINE TEST is a method to test whether a function is One-One or Many-One. As the terms HORIZONTAL  and LINE suggests it is a geometrical (Graphical) method.

It tests whether any HORIZONTAL LINE cuts the graph of the function exactly once or not, if the test is positive, means, if there is only one point of intersection then the Function is One – One, otherwise it is Many – One.

e.g.

Case1.

Y = 2x+3

Graph of y = 2x+3

Example of a One-One Function, as no HORIZONTAL LINE intersects the graph more than once

Y = x^2 -3

Graph of y = x2 - 3

Example of a Many-One Function, as  HORIZONTAL LINEs intersects the graph more than once( Twice)

Solving an Equation using HORIZONTAL LINE TEST

The solution to any equation is the values of x for which y = 0, or the X coordinates of the points of intersection of the HORIZONTAL LINE, y =0 with the graph of the corresponding function.

From Case 1 above it can be seen that there is only one solution x = -3/2

And

From Case 2 above it can be seen that there are two solutions x = √3 and x= -√3

HORIZONTAL LINE TEST to find the values of x for any y of the function y = f(x)

Drawing a HORIZONTAL LINE along the required value of y, we can find the corresponding values of x.

eg.

Figure 1 shows the value of x=0, when y = 3  (point of intersection of the HORIZONTAL LINE y =3 and the graph of the function y = 2x +3)



Figure 2 shows the values of x= ± √ 6 , when y = 3  (point of intersection of the HORIZONTAL LINE y =3 and the graph of the function y = x2 -3)


My forthcoming post is on math word problems for 6th grade and cat exam pattern 2013 will give you more understanding about Algebra.


HORIZONTAL LINE TEST- the primary test for the Existance of Inverse

A function has inverse if and only if it is One-One and On-To

HORIZONTAL LINE TEST determines whether the first condition, one- one is satisfied or not , if the HORIZONTAL LINE TEST fails, then there do not exist any inverse for the function.