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Transformations of Functions I

Transformations of Functions I

A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...

Transformations of Functions II

Transformations of Functions II

Transformations in mathematics alter the position or orientation of a function’s graph while preserving its fundamental shape. One important type of transformation is the horizontal shift, which involves modifying the input variable within a function’s equation. This operation affects where outputs occur along the horizontal axis but does not alter the function’s overall structure.A horizontal shift is achieved by replacing the input variable x with either x + c or x - c,...

Transformations of Functions III

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Related Experiment Video

Updated: May 6, 2026

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Methods to Explore the Influence of Top-down Visual Processes on Motor Behavior

Published on: April 16, 2014

Direct visuomotor transformations for reaching.

Christopher A Buneo¹, Murray R Jarvis, Aaron P Batista

¹Division of Biology, California Institute of Technology, Pasadena, CA 91125, USA.

|April 12, 2002

Summary

This summary is machine-generated.

The posterior parietal cortex (PPC) transforms visual target locations using both eye and hand reference frames. This suggests direct coordinate transformations within the PPC for visually guided reaching.

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Last Updated: May 6, 2026

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Area of Science:

Neuroscience
Cognitive Neuroscience
Motor Control

Background:

The posterior parietal cortex (PPC) is implicated in sensorimotor transformations for visually guided reaching.
PPC damage causes reaching deficits without primary visual or motor impairments.
PPC neurons integrate visual, eye position, and limb position signals.

Purpose of the Study:

To investigate how the posterior parietal cortex (PPC) transforms visual target locations.
To determine if the PPC directly transforms target locations between eye- and hand-centered coordinates.

Main Methods:

Electrophysiological recordings from neurons in dorsal area 5 of the PPC and the parietal reach region (PRR) in monkeys.
Analysis of neuronal responses to remembered target locations relative to eye and hand positions.

Main Results:

In dorsal area 5 of the PPC, remembered target locations are represented relative to both eye and hand positions.
Data from the PRR suggest a transformation achieved by subtracting hand location from target location in eye-centered coordinates.

Conclusions:

The PPC directly transforms target locations between eye- and hand-centered reference frames.
This direct transformation mechanism in the PPC facilitates visually guided reaching.