Download presentation

1
Evaluating Functions

2
**Example Remember this example… If g(x) = x2 + 2x, evaluate g(x – 3)**

g(x-3) = (x2 – 6x + 9) + 2x - 6 g(x-3) = x2 – 6x x - 6 g(x-3) = x2 – 4x + 3 What does this mean?

3
** g(x) = x2 + 2x g(x-3) = x2 – 4x + 3 x = -b = 4 x = -b = -2 = 2**

2a x = -b 2a = 4 2(1) = -2 2(1) = 2 = -1 y = (2)2 – 4(2) + 3 = -1 y = (-1)2 + 2(-1) = -1 Vertex = (-1,-1) Vertex = (2,-1) Pattern = 1,3,5 Pattern = 1,3,5

4
**This leads us into transformations…**

Once you know f(x), then f(x) + c f(x) – c f(x + c) f(x - c) all indicate a transformation.

5
**There are two kinds of transformations:**

Rigid Non-rigid

6
Vocabulary: Rigid Transformation – a shift, slide or reflection of a graph. Non-rigid Transformation – a distortion of a graph by vertical or horizontal stretching.

7
**Rigid Transformations**

f(x) + c f(x) – c f(x + c) f(x - c) -f(x) f(-x) All maintain the exact same shape of the graph. The graph is just repositioned.

8
f(x) + c Moves up c squares. (Adding c to all y’s) f(x) - c Moves down c squares. (Subtracting c from all y’s) f(x + c) Moves left c squares. (Subtracting c from all x’s) f(x - c) Moves right c squares. (Adding c to all x’s)

9
-f(x) Reflects over the x-axis . f(-x) Reflects over the y-axis.

10
**Graph f(x-2) in a different color, but on the same grid.**

Let’s try: f(x) = x2 Graph it in pencil. Graph f(x-2) in a different color, but on the same grid. Graph f(x) – 4 in a different color. Graph -f(x) in a different color. Graph f(x + 3) + 1 in a different color.

11
**Graph f(x-1) in a different color, but on the same grid.**

Let’s try: f(x) = |x| Graph it in pencil. Graph f(x-1) in a different color, but on the same grid. Graph f(x) +2 in a different color. Graph -f(-x) + 1 in a different color. Graph -f(x - 1) in a different color.

12
**Graph -f(x) in a different color, but on the same grid.**

Let’s try: f(x) = x Graph it in pencil. Graph -f(x) in a different color, but on the same grid. Graph f(-x) -1 in a different color. Graph f(x + 3) + 1 in a different color. Graph -f(x) - 1 in a different color.

13
**Graph f(x - 1) + 3 in a different color, but on the same grid.**

Let’s try: f(x) = 3x – 1, x > 0 x + 1, x < 0 Graph it in pencil. Graph f(x - 1) + 3 in a different color, but on the same grid. Graph -f(x + 2) in a different color. Graph f(x) -3 in a different color. Graph f(-x) in a different color.

14
**Non - Rigid Transformations**

f(nx) nf(x) These distort the shape of the graph.

15
**non-rigid transformations work.**

Let’s see how non-rigid transformations work. f(x) = |x| 2f(x) f(2x) x y x y x y Notice what happened to the y-value…

16
nf(x) All the y’s of f(x) get multiplied by n. f(nx) All the x’s of f(x) get divided by n.

17
**Graph f(2x) in a different color, but on the same grid.**

Let’s try: f(x) = x2 Graph it in pencil. Graph f(2x) in a different color, but on the same grid. Graph 2f(x) in a different color. Graph 1/2f(x) in a different color. Graph f(1/2x) in a different color.

18
**Let’s create a unique shape and try one more time.**

Similar presentations

Presentation is loading. Please wait....

OK

UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH

UNIT 1 REVIEW of TRANSFORMATIONS of a GRAPH

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google