vertical translation

(noun)

A shift of the function along the $y$-axis.

Related Terms

Examples of vertical translation in the following topics:

  • Translations

    • A translation of a function is a shift in one or more directions.
    • In algebra, this essentially manifests as a vertical or horizontal shift of a function.
    • To translate a function vertically is to shift the function up or down.
    • In general, a vertical translation is given by the equation:
    • Let's use a basic quadratic function to explore vertical translations.

  • Indefinite Integrals and the Net Change Theorem

    • Essentially, the graphs of antiderivatives of a given function are vertical translations of each other, with each graph's location depending upon the value of $C$.

  • Antiderivatives

    • Essentially, the graphs of antiderivatives of a given function are vertical translations of each other, with each graph's location depending upon the value of $C$.

  • Symmetry of Functions

    • The image below shows an example of a function and its symmetry over the $x$-axis (vertical reflection) and over the $y$-axis (horizontal reflection).  
    • A function can have symmetry by reflecting its graph horizontally or vertically.  
    • This type of symmetry is a translation over an axis.

  • The Vertical Line Test

    • The vertical line test is used to determine whether a curve on an $xy$-plane is a function
    • If, alternatively, a vertical line intersects the graph no more than once, no matter where the vertical line is placed, then the graph is the graph of a function.
    • The vertical line test demonstrates that a circle is not a function.
    • Thus, it fails the vertical line test and does not represent a function.
    • Any vertical line in the bottom graph passes through only once and hence passes the vertical line test, and thus represents a function.

  • Regulation of Sigma Factor Translation

    • The regulation of expression of sigma factors occurs at transcriptional, translational, and post-translational levels as dictated by the cellular environment and the presence or absence of numerous cofactors.
    • Specifically, the translational control of the sigma factor is a major level of control.
    • The translational control of sigma factors involves the presence and function of small noncoding RNAs.
    • The small noncoding RNAs are able to specifically increase the amount of rpoS mRNA that undergoes translation.
    • These RNAs can induce activation of rpoS translation.

  • The Act of Translating: Hijacking Authority

    • Finally, the fifth variation, $T \rightarrow X + Y$ , refers to the act of translating a thought from one language to another.
    • The authenticity of the translation then becomes of secondary importance at best, and the principal issue becomes: what words, labeled as the results of translation, will be most likely to encourage the people who read them to act in the ways desired by the translator?
    • The most obvious potential for this second kind of translation—translation with a hidden agenda—exists when the words being translated come from a document which people tend to regard as authoritative. * When the document being "translated" is in the same language as that it is translated into, we normally use the term interpret rather than translate, but here too there are abundant opportunities for a hidden agenda. **
    • *The Bible is probably the most obvious target for translations based on a "hidden agenda".
    • **An authoritative document frequently subjected to hidden agenda translations is the US Constitution.

  • Cancer and Translational Control

    • There are many examples of translational or post-translational modifications of proteins that arise in cancer.
    • Modifications are found in cancer cells from the increased translation of a protein to changes in protein phosphorylation to alternative splice variants of a protein.

  • Translation Manager

    • In software projects, "translation" can refer to two very different things.
    • Part of the reason the translation manager is necessary is that translators are a different demographic from developers.
    • The translation manager makes sure that the translations happen in a way that does not interfere unnecessarily with regular development.
    • When a new volunteer shows up offering to translate Subversion to, say, Malagasy, the translation manager has to either hook him up with someone who posted six months ago expressing interest in doing a Malagasy translation, or else politely ask the volunteer to go find another Malagasy translator to work with as a partner.
    • Conversations between the translation manager and the developers, or between the translation manager and translation teams, are usually held in the project's original language—that is, the language from which all the translations are being made.

  • Segmented bar and mosaic plots

    • The column proportions of Table 1.36 have been translated into a standardized segmented bar plot in Figure 1.38(b), which is a helpful visualization of the fraction of spam emails in each level of number.
    • We can again use this plot to see that the spam and number variables are associated since some columns are divided in different vertical locations than others, which was the same technique used for checking an association in the standardized version of the segmented bar plot.