Download presentation

Presentation is loading. Please wait.

Published byElizabeth Gallagher Modified over 4 years ago

1
Algebra II Piecewise Functions Edited by Mrs. Harlow

2
2-6: Special Functions Constant Identity Absolute Value Step/Greatest Integer Piecewise

3
Constant Function: A linear function in the form y = b. y = 3

4
Identity Function: A linear function in the form y = x. y=x

5
Up to now, weve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are called piecewise functions.

6
One equation gives the value of f(x) when x 1 And the other when x>1

7
Evaluate f(x) when x=0, x=2, x=4 First you have to figure out which equation to use You NEVER use both X=0 This one fits into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9

8
Graph: For all xs < 1, use the top graph (to the left of 1) For all xs 1, use the bottom graph (to the right of 1)

9
x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

10
Graph:

11
Greatest Integer Function: A function in the form y = [x] 246–2–4–6x 2 4 6 –2 –4 –6 y y=[x] Note: [x] means the greatest integer less than or equal to x. For example, the largest integer less than or equal to -3.5 is -4.

12
Greatest Integer Function: A function inthe form y = [x] Graph y= [x] + 2 by completing the t-table: x y -3 - 2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25 0 1 246–2–4–6x 2 4 6 –2 –4 –6 y x y -3 y= [-3]+2=-1 - 2.75 y= [-2.75]+2=-1 -2.5 y= [-2.5]+2=-1 -2.25 y= [-2.25]+2=-1 -2 y= [-2]+2 =0 -1.75 y= [-1.75]+2=0 -1.5 y= [-1.5]+2=0 -1.25 y= [-1.25]+2=0 -1 y= [-1]+2=1 0 y= [0]+2=2 1 y= [1]+2=3

13
Step Functions

15
Graph :

17
Labor costs at the Fix-It Auto Repair Shop are $60 per hour or any fraction thereof. Draw a graph that represents this situation.

18
Assignment

Similar presentations

OK

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

© 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

Ppt on unsustainable to sustainable development Ppt on network theory documentary Ppt on e learning system Ppt on commercial use of microorganisms in the field Free ppt on management of natural resources Ppt on single phase and three phase dual converter circuit Ppt on peak load pricing Ppt on earth and space book Ppt on diodes and transistors Ppt on power sharing in democracy the will of the majority