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:
“I am a sort of martyr, as you see,
A horizontal monument to patience.
The calves of waitresses parade about
My helpless head upon this sodden floor.
Well, I am down again, but not yet out.
O sweet frustrations, I shall be back for more.”
—Richard Wilbur (b. 1921)
“There’s something like a line of gold thread running through a man’s words when he talks to his daughter, and gradually over the years it gets to be long enough for you pick up in your hands and weave into a cloth that feels like love itself. It’s another thing, though, to hold up that cloth for inspection.”
—John Gregory Brown (20th century)
“The final test of a novel will be our affection for it, as it is the test of our friends, and of anything else which we cannot define.”
—E.M. (Edward Morgan)
“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)