Cardhop 1.3.6 October 22, 2020
- Fixed a potential crash when creating or updating contacts
- Fixed a performance issue when there are many contacts with custom labels
- Various fixes and improvements
Cardhop 1.3.5 September 8, 2020
- Improved handling of duplicate information being entered into the parser
- Fixed an issue where text entered into the parser would appear offset in some situations
- Fixed an issue where the print preview wouldn't appear in some situations
- Various fixes and improvements
Cardhop 1.3.4 May 18, 2020
- Added option to filter by job title in smart groups
- Emailing a contact will include the name of the contact in the new message window
- Improved calculation of age for Chinese lunar birthdays
- Fixed an issue where contact details wouldn't appear correctly when in full screen
- Fixed an issue where All Contacts wouldn't appear for some Exchange accounts
- Various fixes and improvements
Cardhop 1.3.3 December 10, 2019
- Cardhop will ask you to reauthorize your G Suite account if Google Admin API access has been disabled by your organization
- Added Copy Picture option when clicking on a contact's photo
- Improved editing alternate birthday fields
- Fixed a potential crash when printing envelopes
- Various fixes and improvements
Cardhop 1.3.2 August 14, 2019
- File size of exported vCards with images are now smaller
- Fixed some potential crashes
- Various fixes and improvements
Cardhop 1.3.1 July 11, 2019
- Added paper orientation options when printing envelopes and lists
- Added GitHub to list of social networks
- Fixed a crash when looking up contacts on Gravatar
- Various fixes and improvements
Cardhop 1.3 June 18, 2019
- Preference to show nicknames in contact lists
- Support for sending messages to groups with the parser (e.g. message /friends Hey guys)
- New templates when adding new smart groups to make it easier to quickly add new smart groups
- Various fixes and improvements
Cardhop 1.2.5 May 21, 2019
- Fixed an issue connecting to some Exchange 2013 directories
- Hid company checkbox on Exchange because Exchange doesn't support company-only contacts
- Various fixes and improvements
Cardhop 1.2.4 May 10, 2019
- Fixed a potential crash with some Chinese names
- Various fixes and improvements
Cardhop 1.2.3 May 1, 2019
- Ages are now shown next to birthdays in the list
- Can now drag contacts from directories to accounts or groups to make a copy of the directory contact
- Pasting emails containing mailto: links will automatically remove the mailto: prefix
- Various fixes and improvements
Cardhop 1.2.2 April 11, 2019
- WhatsApp action now opens the WhatsApp app if it is installed
- Better sorting of options in Add Field menu
- Better handling of sorting contacts with accents and non-Latin characters
- Various fixes and improvements
Cardhop 1.2.1 March 30, 2019
- Fixed an issue with Exchange and Office 365 directory contacts not showing phone numbers or emails
- G Suite directory contacts will now show additional information and photos
- Improved matching of contacts with accents when searching
- Fixed a crash on macOS 10.11 and 10.12
Cardhop 1.2 March 27, 2019
- Directories: Add Google, Exchange, and Office 365 directories to look up users on Google Contacts, G Suite, and Exchange Global Address List
- Favorites! Mark commonly used contacts as favorites. Favorites sync between all devices, including with Cardhop for iOS
- Added Copy Contact URL option to copy a URL which will show a contact in Cardhop from another app
- Fixed a potential crash when using smart groups on macOS Mojave
- Improved matching of contacts that have an email address but no first or last name
- Various fixes and improvements
Cardhop 1.1.6 October 25, 2018
- Fixed a potential crash when using smart groups on macOS Mojave
- Improved matching of contacts that have an email address but no first or last name
- Various fixes and improvements
Cardhop 1.1.5 September 25, 2018
- Support for Dark Mode on macOS Mojave
- Improved handling of names entered as Last, First (such as Smith, Alice)
- Various fixes and improvements
Cardhop 1.1.4 August 7, 2018
- Fixed a crash on macOS El Capitan
- Various fixes and improvements
Cardhop 1.1.3 August 3, 2018
- Added Instagram as a social profile type
- Added an option to skip already used labels when printing a sheet of labels
- Pressing return when a contact is selected will now begin editing the contact
- Dragging and dropping a contact into another app will now drop the contact name and a link to the contact
- Selecting a contact picture from a file will now show options to crop the picture
- Fixed an issue when using Skype to call phone numbers without a country code
- Various fixes and improvements
Cardhop 1.1.2 May 8, 2018
- Fixed an issue where adding contacts didn't work for some people
- Fixed an issue where creating a contact with emoji didn't work
- Fixed some DYMO labels printing with the wrong orientation
- Various fixes and improvements
Cardhop 1.1.1 May 5, 2018
- Added a smart group option to match contacts that are a company or a person
- Template preferences now apply to new contacts created by Cardhop's parser
- Fixed smart group criteria for 'is set' and 'is not set' not working in some cases
- Fixed an issue where Cardhop could hang at launch in certain situations
- Various fixes and improvements
Cardhop 1.1 May 2, 2018
- Full support for French, German, Italian, Spanish, English, and Japanese (including parsing and address/phone formats)
- Smart groups: Create dynamic smart groups that automatically update based on specific search criteria
- Template preferences to customize fields and labels for new contacts
- Printing support: Print customized envelopes, labels, and lists of contacts
- Quick Action for printing: Type “print” or use a Quick Action button to quickly print a contact or group
- “Add Notes with Timestamp” option to quickly insert the current date and time into the notes of a contact
- Typing into a related name field now suggests other names in your contacts
- Various fixes and improvements
Cardhop 1.0.7 February 27, 2018
- Various fixes and improvements
Cardhop 1.0.6 January 23, 2018
- Improved parsing of phone numbers with extensions
- Fixed a crash when opening preferences on macOS El Capitan
- Various fixes and improvements
Cardhop 1.0.5 December 19, 2017
- Added option to set the default country calling code for phone numbers
- Improved parsing of email signatures that include images
- Fixed an issue where birthdays wouldn't appear at the end of the year
- Various fixes and improvements
Cardhop 1.0.4 December 12, 2017
- Fixed a crash when encountering some types of contact data
Cardhop 1.0.3 December 10, 2017
- Fixed an issue where the default account setting wasn't saved
- Fixed some contact parsing issues
- Fixed an issue where the end of very long notes could get hidden
- Fixed an issue where deleted info from a contact could return if changes were detected in Contacts
- Improved compatibility with Skype 8 when dialing phone numbers
- Various fixes and improvements
Cardhop 1.0.2 November 8, 2017
- Improved editing of linked contacts that are on multiple accounts
- Added AppleScript support for sending text to Cardhop
- Added Skype for Business action
- Fixed first and last name order when viewing Chinese, Japanese, and Korean contacts
- Various fixes and improvements
Cardhop 1.0.1 October 21, 2017
- Skype action now allows calling phone numbers through Skype
- Increased maximum allowed width of groups sidebar
- Fixed some crashes when encountering invalid contact data
- Fixed a crash when using Share My Card
- Various fixes and improvements
Cardhop 1.0 October 18, 2017
- Initial release
Cardhop 1.2.3 MacOS Full macOS;; KoLomPC; 0 comments; 514 views; Hi everyone and have a nice day as you know we have opened the file sharing server so that you can quickly and without delay download the files, unfortunately for financial reasons we have to close it, if you want to continue to use it for downloading files. Cardhop's magical parsing engine is incredibly intuitive, letting you search, add, edit, and interact with your contacts using a simple sentence! Just type in 'John G' and John's card will instantly appear. Or enter 'Sarah Smith [email protected]' and Cardhop will add a new contact to Sarah's card. Cardhop sweats the details in the individual card view as well. The notes field, buried in Apple’s Contacts, is always accessible as a small overlay. Superior visual design differentiates methods of contact – blue buttons for written; green for calls. Bold headings and icons draw the eye. Even tapping fields is better. Cardhop lets you search, add, edit, and interact with your contacts in a fun and interactive way. Desperados: Wanted Dead or Alive 1.0.2.thqn (22619) October 11.
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Composition of Functions:
Composing with Sets of Points (page 1 of 6)
Composing with Sets of Points (page 1 of 6)
Sections: Composing functions that are sets of point, Composing functions at points, Composing functions with other functions, Word problems using composition, Inverse functions and composition
Until now, given a function f(x), you would plug a number or another variable in for x. You could even get fancy and plug in an entire expression for x. For example, given f(x) = 2x + 3, you could find f(y2 – 1) by plugging y2 – 1 in for x to get f(y2 – 1) = 2(y2 – 1) + 3 = 2y2 – 2 + 3 = 2y2 + 1.
In function composition, you're plugging entire functions in for the x. Money pro 1 9 – manage money like a problem. In other words, you're always getting 'fancy'. But let's start simple. Instead of dealing with functions as formulas, let's deal with functions as sets of (x, y) points:
- Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and
let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.
Find (i)f (1), (ii) g(–1), and (iii) (gof )(1).
(i) This type of exercise is meant to emphasize that the (x, y) points are really (x, f (x)) points. To find f (1), I need to find the (x, y) point in the set of (x, f (x)) points that has a first coordinate of x = 1. Then f (1) is the y-value of that point. In this case, the point with x = 1 is (1, –1), so:
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f (1) = –1
(ii) The point in the g(x) set of point with x = –1 is the point (–1, –2), so:
g(–1) = –2
(iii) What is '(gof )(1)'? This is read as 'g-compose-f of 1', and means 'plug 1 into f, evaluate, and then plug the result into g'. The computation can feel a lot easier if I use the following, more intuitive, formatting:
(gof )(1) = g( f(1))
Now I'll work in steps, keeping in mind that, while I may be used to doing things from the left to the right (because that's how we read), composition works from the right to the left (or, if you prefer, from the inside out). So I'll start with the x = 1. I am plugging this into f(x), so I look in the set of f(x) points for a point with x = 1. The point is (1, –1). This tells me that f(1) = –1, so now I have: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved
(gof )(1) = g( f(1)) = g(–1)
Tweetbot for twitter 2 3 4. Working from the right back toward the left, I am now plugging x = –1 (from 'f(1) = –1') into g(x), so I look in the set of g(x) points for a point with x = –1. That point is (–1, –2). This tells me that g(–1) = –2, so now I have my answer:
(gof )(1) = g( f(1)) = g(–1) = –2
Note that they never told us what were the formulas, if any, for f(x) or g(x); we were only given a list of points. But this list was sufficient for answering the question, as long as we keep track of our x- and y-values.
Cardhop 1 2 2 0 25
- Let f = {(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} and
let g = {(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}.
Find (i) ( fog)(0), (ii)( fog)(–1), and (iii)(gof )(–1).
(i) To find ( fog)(0), ('f-compose-g of zero'), I'll rewrite the expression as:
( fog)(0) = f(g(0))
This tells me that I'm going to plug zero into g(x), simplify, and then plug the result into f(x). Looking at the list of g(x) points, I find (0, 2), so g(0) = 2, and I need now to find f(2). Looking at the list of f(x) points, I find (2, –3), so f(2) = –3. Then:
( fog)(0) = f(g(0)) = f(2) = –3
(ii) The second part works the same way:
( fog)(–1) = f(g(–1)) = f(–2) = 3
(iii) I can rewrite the composition as (gof )(–1) = g( f(–1)) = g(1).
Uh-oh; there is no g(x) point with x = 1, so it is nonsense to try to find the value of g(1). In math-speak, g(1) is 'not defined'; that is, it is nonsense.Then (gof )(–1) is also nonsense, so the answer is:
(gof )(–1) is undefined.
Part (iii) of the above example points out an important consideration regarding domains and ranges. It may be that your composed function (the result you get after composing two other functions) will have a restricted domain, or at least a domain that is more restricted than you might otherwise have expected. This will be more important when we deal with composing functions symbolically later.
Another exercise of this type gives you two graphs, rather than two sets of points, and has you read the points (the function values) from these graphs.
- Given f(x) and g(x) as shown below, find ( fog)(–1).
In this case, I will read the points from the graph. I've been asked to find ( fog)(–1) = f(g(–1)). This means that I first need to find g(–1). So I look on the graph of g(x), and find x = –1. Tracing up from x = –1 to the graph of g(x), I arrive at y = 3. Then the point (–1, 3) is on the graph of g(x), and g(–1) = 3.
Now I plug this value, x = 3, into f(x). To do this, I look at the graph of f(x) and find x = 3. Tracing up from x = 3 to the graph of f(x), I arrive at y = 3. Then the point (3, 3) is on the graph of f(x), and f(3) = 3.
Then( fog)(–1) = f(g(–1)) = f(3) = 3.
Cardhop 1 2 2 0 9
- Given f(x) and g(x) as shown in the graphs below, find (gof )(x) for integral values of x on the interval –3 <x< 3.
f(x): | g(x): |
This is asking me for all the values of (gof )(x) = g( f(x)) for x = –3, –2, –1, 0, 1, 2, and 3. So I'll just follow the points on the graphs and compute all the values:
(gof )(–3) = g( f(–3)) = g(1) = –1
I got this answer by looking at x = –3 on the f(x) graph, finding the corresponding y-value of 1 on the f(x) graph, and using this answer as my new x-value on the g(x) graph. That is, I looked at x = –3 on the f(x) graph, found that this led to y = 1, went to x = 1 on the g(x) graph, and found that this led to y = –1. Similarly:
(gof )(–2) = g( f(–2)) = g(–1) = 3
(gof )(–1) = g( f(–1)) = g(–3) = –2
(gof )(0) = g( f(0)) = g(–2) = 0
(gof )(1) = g( f(1)) = g(0) = 2
(gof )(2) = g( f(2)) = g(2) = –3
(gof )(3) = g( f(3)) = g(3) = 1
(gof )(–1) = g( f(–1)) = g(–3) = –2
(gof )(0) = g( f(0)) = g(–2) = 0
(gof )(1) = g( f(1)) = g(0) = 2
(gof )(2) = g( f(2)) = g(2) = –3
(gof )(3) = g( f(3)) = g(3) = 1
Cardhop 1 2 2 0
You aren't generally given functions as sets of points or as graphs, however. Generally, you have formulas for your functions. So let's see what composition looks like in that case.. Bettersnaptool 1 9 3.
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Cite this article as: | Stapel, Elizabeth. 'Composing with Sets of Points.' Purplemath. Available from https://www.purplemath.com/modules/fcncomp.htm. Accessed [Date] [Month] 2016 |