1 / 9

Graphing Rational Functions Through Transformations

Graphing Rational Functions Through Transformations. Rational parent function. Vertical and horizontal shifts. The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): H(x)=f( x-c ) horizontal shift c units to the right

eadoin
Download Presentation

Graphing Rational Functions Through Transformations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Graphing Rational Functions Through Transformations

  2. Rational parent function

  3. Vertical and horizontal shifts • The following changes in the functions y=f(x) will produce the stated shifts in the graph of y=f(x): • H(x)=f(x-c) horizontal shift c units to the right • H(x)=f(x+c) horizontal shift c units to the left • H(x)=f(x)-c vertical shift c units downward • H(x)=f(x)+c vertical shift c units upward

  4. Reflections • The following changes in the function y=f(x) will produce the stated reflections in the graph of y=f(x): • H(x)=-f(x) reflection with respect to the x-axis • H(x)=f(-x) reflection with respect to the y-axis

  5. Nonrigid transformations • Nonrigid transformations actually distort the shape of the graph, instead of just shifting or reflecting it. • Nonrigid transformations of y=f(x) come from equations of the form y=cf(x). • If c>1, then there is a vertical stretch of the graph of y=f(x). • If 0<c<1, then there is a vertical shrink • We will discuss horizontal extensions and compressions at a further date.

  6. Graphing based on transformations • Tell the transformations that occurred and graph the following

  7. Answer • Transformations and graph • Up 3 (HA), right 5 (VA), reflect over x-axis, and stretch by 2

  8. Graphing based on transformations • Tell the transformations that occurred and graph the following

  9. Answer • Transformations and graph • Down 4 (HA), left 2 (VA), reflect over x-axis

More Related