1 / 12

GCSE Revision 101

GCSE Revision 101. Maths Transforming Graphs. © Daniel Holloway. The Basics. Transforming graphs is not too dissimilar from transforming shapes. Whereas you can translate, rotate, reflect and enlarge shapes; you can translate , stretch and reflect graphs.

bozica
Download Presentation

GCSE Revision 101

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. GCSE Revision 101 Maths Transforming Graphs © Daniel Holloway

  2. The Basics Transforming graphs is not too dissimilar from transforming shapes. Whereas you can translate, rotate, reflect and enlarge shapes; you can translate, stretch and reflect graphs. We use the notation f(x) to denote a function of x. A function of x is any algebraic expression where x is the only variable.

  3. The Basics There are six rules you need to learn about transforming graphs. To show these rules, we will use the following graph. This is the graph y = f(x)

  4. Translating Graphs Rule 1: This is a translation of the graph in the vector ( ) in the y-direction 0 a y = f(x) + a

  5. Translating Graphs Rule 2:This is a translation of the graph in the vector ( ) in the x-direction a 0 y = f(x – a)

  6. Stretching Graphs Rule 3:This is a stretch of the graph by a scale factor of k in the y-direction Note thatthey crossat the x axis y = kf(x)

  7. Stretching Graphs Rule 4:This is a stretch of the graph by a scale factor of 1/t in the x-direction Note thatthey crossat the yaxis y = f(tx)

  8. Reflecting Graphs Rule 5:This is a reflection of the graph in the x-axis y = -f(x)

  9. Reflecting Graphs Rule 6:This is a reflection of the graph in the y-axis y = f(-x)

  10. Examples of Transformations y y 5 5 0 0 x -5 5 x -5 5 The grid shows the graph of y=x2 for -2 ≤ x ≤ 2 The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid. y = (x + 3) 2

  11. Examples of Transformations y y 5 5 0 0 x -5 5 x -5 5 The grid shows the graph of y=x2 for -2 ≤ x ≤ 2 The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid. y = x2 - 2

  12. Examples of Transformations y y 5 5 0 0 x -5 5 x -5 5 The grid shows the graph of y=x2 for -2 ≤ x ≤ 2 The dotted line shows the same graph. Describe the transformation taking it to the new line on the grid. y = 2x2

More Related