Download presentation

Presentation is loading. Please wait.

Published byJasmine Callahan Modified over 4 years ago

1
One-to-One Functions Recall the definition of a function: A function is a relation (set of ordered pairs) such that for each x-value, there is _________________. And recall the graph of functions: If a relation is a function, its graph must pass the __________________. So, what do you think the definition of a one-to-one function is? A one-to-one (denoted by 1-1) function is a function such that for ____________________________ _______________. Or we can say, a 1-1 function is a relation such that not only for x-value there is a corresponding y-value, but also for ___________________________. What do you think the graph of a 1-1 function must pass? Since a 1-1 function is a function, so it must pass the Vertical Line Test. However, in order for a function to be 1-1, it also needs to pass the __________________. Which of the five graphs are 1-1 functions? ____________ Conclusion: If a function is 1-1, its graph must be strictly __________ or strictly __________.

2
Inverse Functions Two functions, f(x) and g(x) are called inverse functions f(g(x)) = x and g(f(x)) = x. How do we show a pair of functions are inverse functions? Examples: 1. f(x) = 2x f(x) = x2 + 3 (x 0) g(x) = ½x – 2 g(x) = Sketch each of the pair inverse functions on the same axes. Is there a line of symmetry and what is it? ___________________ What happen if we didn’t include the stated (or restricted) domain for example 2? What will its “inverse” graph be if we just flip it over the line y = x? Conclusion: In order for a function to have an inverse function, the function itself must be a _____ function. If not, though we still can plot the “inverse,” we can’t call it the inverse function.

3
**Inverse Functions (cont’d)**

Q: Given a one-to-one function, f(x), how can we find its inverse function (which is commonly denoted by f –1(x), instead of g(x))? A: Follow this 4-step process: Step 1: Replace f(x) by y. Step 2: Interchange x and y (i.e., x becomes y, y becomes x). Step 3: Solve y in terms of x (this is the only step that really involves algebra). Step 4: Replace y by the notation f –1(x). Given f(x), find its inverse function f –1(x). 1. f(x) = 2x f(x) = x2 + 3 (x 0) If the graph of a 1-1 function is given, how do we sketch its inverse function? ________________________ Given the graph of a 1-1 function, sketch its inverse function

Similar presentations

OK

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 2 Graphs and Functions.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 2 Graphs and Functions.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on computer malwares anti-malware Ppt on micro operations Ppt on job rotation job Ppt on soil microbial biomass carbon Ppt on places in our neighbourhood living Ppt on retail marketing Ppt on mass media in education Ppt on retail marketing strategy Ppt on distance formula and midpoint Ppt on industrial employment standing order act 1946