Horizontal Line Test - Horizontal Line Test in Calculus

Horizontal Line Test in Calculus

Given a function (i.e. from the real numbers to the real numbers), we can decide if it is injective by looking at horizontal lines that intersect the function's graph. If any line intersects the graph in more than one point, the function is not injective. To see this, note that the points of intersection have the same y-value (because they lie on the line ) but different x values, which by definition means the function cannot be injective.



Passes the test (injective)


Fails the test (not injective)

Read more about this topic:  Horizontal Line Test

Famous quotes containing the words horizontal, line, test and/or calculus:

    In bourgeois society, the French and the industrial revolution transformed the authorization of political space. The political revolution put an end to the formalized hierarchy of the ancien regimé.... Concurrently, the industrial revolution subverted the social hierarchy upon which the old political space was based. It transformed the experience of society from one of vertical hierarchy to one of horizontal class stratification.
    Donald M. Lowe, U.S. historian, educator. History of Bourgeois Perception, ch. 4, University of Chicago Press (1982)

    That’s the down-town frieze,
    Principally the church steeple,
    A black line beside a white line;
    And the stack of the electric plant,
    A black line drawn on flat air.
    Wallace Stevens (1879–1955)

    To answer a question so as to admit of no reply, is the test of a man.
    Ralph Waldo Emerson (1803–1882)

    I try to make a rough music, a dance of the mind, a calculus of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.
    Judith Johnson Sherwin (b. 1936)