Name: Transforming Algebraic Functions
Uploaded: 2019-07-19
Duration: 21 min 54 s
Description: We know the basics of graphing algebraic functions; it's time to learn some tricks that will come in handy as we graph different functions.

Question

What are the three transformations for linear and quadratic graphs?

Accepted Answer

Following are the three transformations for linear and quadratic graphs:

Translation: A translation occurs when every point on a graph moves by the same amount in the same direction. To translate a curve horizontally is to shift the function left or right. To translate a curve vertically is to shift the function up or down.

Dilation: A dilation is a stretch or a compression. If a graph undergoes dilation parallel to the $x$ -axis, all the $x$ -values are multiplied by the same scale factor. Similarly, if it is dilated parallel to the $y$ -axis, all the $y$ -values are multiplied by the same scale factor.

Reflection: Another transformation that can be applied to a function is a reflection over the $x$ - or $y$ -axis. A vertical reflection reflects a graph vertically across the $x$ -axis, while a horizontal reflection reflects a graph horizontally across the $y$ -axis.

Notice that the vertical reflection produces a new graph that is a mirror image of the base or original graph about the $x$ -axis. The horizontal reflection produces a new graph that is a mirror image of the base or original graph about the $y$ -axis.

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Changing graphs

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Changing graphs

Questions from Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 2: Changing graphs with Hints & Solutions

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