Download presentation

Presentation is loading. Please wait.

Published byWill Acors Modified over 2 years ago

1
Reflections and Symmetry Lesson 5.2

2
Flipping the Graph of a Function Given the function below We wish to manipulate it by reflecting it across one of the axes Across the x-axis Across the y-axis

3
Flipping the Graph of a Function Consider the function f(x) = 0.1*(x 3 - 9x 2 + 5) : place it in y1(x) graphed on the window -10 < x < 10 and -20 < y < 20

4
Flipping the Graph of a Function specify the following functions on the Y= screen: y2(x) = y1(-x) dotted style y3(x) = -y1(x) thick style Predict which of these will rotate the function about the x-axis about the y-axis

5
Flipping the Graph of a Function Results To reflect f(x) in the x-axis or rotate about To reflect f(x) in the y-axis or rotate about use -f(x) use f(-x) Spreadsheet Demo

6
Even and Odd Functions If f(x) = f(-x) the graph is symmetric across the y-axis It is also an even function

7
Even and Odd Functions If f(x) = -f(x) the graph is symmetric across the x-axis But... is it a function ??

8
Even and Odd Functions A graph can be symmetric about a point Called point symmetry If f(-x) = -f(x) it is symmetric about the origin Also an odd function

9
Applications Consider a frozen yam placed into a hot oven. Think what the graph of the temperature would look like. Sketch the graph of the temperature of the yam. It is frozen at 0 degrees Fahrenheit and the oven is at 300 degrees Fahrenheit. This will be both a flip and a shift of an exponential function

10
Applications This is the function f(x) = 300 - 300(0.97)t It has been flipped about the y-axis Then it has been shifted up Which part did the shift? Which part did the flip?

11
Reflecting in the Line y = x Given the function below: For each (x,y) shown, reverse the values to get (y,x) Plot the (y,x) values and connect the points

12
Reflecting in the Line y = x Results Note: it is not a function.

13
Reflecting in the Line y = x Try it for this graph … will the result be a function or not?

14
Assignment Lesson 5.2 Page 209 Exercises 1 – 31 odd

Similar presentations

Presentation is loading. Please wait....

OK

Quadratic Equations and Problem Solving Lesson 3.2.

Quadratic Equations and Problem Solving Lesson 3.2.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on natural and manmade disaster Skeletal system anatomy and physiology ppt on cells Ppt on uses of water Ppt on beer lambert law units Ppt on m commerce Ppt on network load balancing Ppt on particles of matter attract each other Ppt on limits and derivatives calculus Ppt on file system Ppt on earth dam failures