Vertical Shift

Vertical shift is a graph transformation that moves a function’s output values upward or downward without changing its shape or horizontal position. For a function written as y=f(x), the expression y=f(x)+k produces a vertical shift of k units: positive k moves the graph up, while negative k moves it down. This change affects the range and y-intercept but leaves the domain and x-coordinates of corresponding points unchanged. Understanding vertical shifts helps students compare function graphs, transform equations, and interpret mathematical models where a constant represents a fixed increase or decrease.

Vertical Shift - Related Videos

Education

JoVE Science Education - Physics

Sound Waves and Doppler Shift

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2023

Source: Arianna Brown, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA Waves are disturbances that propagate through a material medium or empty space. Light waves can travel through a vacuum and some forms of matter, and are transverse in nature, which means that the oscillations are perpendicular to the direction of propagation. However, sound waves are pressure waves that travel through an elastic medium like air,...

Vertical Curve: Problem Solving

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2025

Vertical curves provide the transition between two roadway grades, ensuring safety, comfort, and functionality. Calculating elevations at specific stations along the curve involves several systematic steps based on the curve's geometry and provided design parameters.The vertical curve is defined by its length, grades, Point of Vertical Intersection (P.V.I.) location, and P.V.I. elevation. The stations of the Point of Vertical Curvature (P.V.C.), where the curve begins, and the Point of Vertical...

Vertical Marketing Systems

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2024

A Vertical Marketing System (VMS) is the distribution channel arrangement in which producers, wholesalers, and retailers collaborate as a unified system with the goal of enhancing efficiency and effectiveness. This organizational structure allows for better coordination and collaboration between different entities, resulting in increased cost efficiency and economies of scale. There are three main types of VMS: corporate, contractual, and administrative. Each type has its own unique...

Introduction to Vertical Curves

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2025

Vertical curves are parabolic transitions that connect different grades on highways and railroads, ensuring a smooth alignment between back and forward tangents. The back tangent represents the initial grade, while the forward tangent defines the subsequent grade. These curves can be symmetrical, with equal tangent lengths, or nonsymmetrical, with varying lengths. The key points defining a vertical curve include the Point of Vertical Intersection (P.V.I.), where the tangents meet; the Point of...

Electrophoretic Mobility Shift Assay (EMSA)

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2023

The electrophoretic mobility shift assay (EMSA) is a biochemical procedure used to elucidate binding between proteins and nucleic acids. In this assay a radiolabeled nucleic acid and test protein are mixed. Binding is determined via gel electrophoresis which separates components based on mass, charge, and conformation. This video shows the concepts of EMSA and a general procedure, including gel and protein preparation, binding, electrophoresis, and detection. Applications covered in this video...

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