This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
someone asked: On Lesson Check Do you know how number 4 it asks to tell whether each set of ordered pairs in Exercise 1 represents a function and justify my answer, can you further explain? What does it mean by represent a function? A function of what?
Ordered Pairs are.....
a. (0,0) (1,1) (2,2) (3,3) (4,4) b.(0,8) (1,6) (2,4) (3,2) (4,0) c. (3,0) (3,1) (3,2) (3,3) (3,4)
fyi, the lesson check quizzes mix up their questions all the time, so #4 is not always #4!
Recognizing a function is an important, and initially conceptually difficult, task for a beginning algebra student to master... we will touch upon this very topic several times throughout the remainder of this year. In other words, don't worry too much that you are struggling with it a bit EVERYONE DOES!! (including me when I took algebra, which was before text books were invented).
You gave me enuf info to answer your question, so here goes:
Let's dissect (like a frog) the definition of a function.
An (algebraic) function is a relationship that pairs each input value with EXACTLY one output value.
Simply viewed, in choices a and b in your question, the input values (the FIRST value in the ORDERED pairs) are paired with a single output value.
In choice c, the input value of 3 has several different output values.
A function machine works on the premise that it produces a specific output value based on the value input. In the case of answer choice c, if I input 3, I am getting different "responses"... therefore, a & b are functions and c is not.
We will discuss this MUCH MORE and there are other ways (including visually/graphically) to tell whether a relation is a function... SO DON'T SWEAT IT and enjoy your Sunday!!!
To answer your second question... more often than not a function will have a pattern of some sort, but a relation can have fairly random looking values and still be a function.
For example: (1,19),(3,-171),(5,-13.2) is a function (1,2),(2,3),(2,4) is not a function because the input value of 2 is paired with two different numbers (3&4).
I kind of get it but I really don't understand it. What I have got from all of this is that a function basically determines another value, representing an input, correct??
Yup... this is a tough concept... it takes awhile for "thinkers" to get this one to sink in. Don't worry too much, you have awhile before the quiz or test.
We will go over it in class again and again each day... slowly but surely it will sink in... no need to memorize or stress... just come to class with an open mind... and keep re-reading the definition of a function each day and look at new examples... we'll get there, slow and steady wins this race!
someone asked:
ReplyDeleteOn Lesson Check Do you know how number 4 it asks to tell whether each set of ordered pairs in Exercise 1 represents a function and justify my answer, can you further explain? What does it mean by represent a function? A function of what?
Ordered Pairs are.....
a. (0,0) (1,1) (2,2) (3,3) (4,4)
b.(0,8) (1,6) (2,4) (3,2) (4,0)
c. (3,0) (3,1) (3,2) (3,3) (3,4)
Would a function be a pattern possibly? Like a. (0,0) (1,1) (2,2) (3,3) (4,4) You add one to x and y each time ??
ReplyDeletefyi, the lesson check quizzes mix up their questions all the time, so #4 is not always #4!
ReplyDeleteRecognizing a function is an important, and initially conceptually difficult, task for a beginning algebra student to master... we will touch upon this very topic several times throughout the remainder of this year. In other words, don't worry too much that you are struggling with it a bit EVERYONE DOES!! (including me when I took algebra, which was before text books were invented).
You gave me enuf info to answer your question, so here goes:
Let's dissect (like a frog) the definition of a function.
An (algebraic) function is a relationship that pairs each input value with EXACTLY one output value.
Simply viewed, in choices a and b in your question, the input values (the FIRST value in the ORDERED pairs) are paired with a single output value.
In choice c, the input value of 3 has several different output values.
A function machine works on the premise that it produces a specific output value based on the value input. In the case of answer choice c, if I input 3, I am getting different "responses"... therefore, a & b are functions and c is not.
We will discuss this MUCH MORE and there are other ways (including visually/graphically) to tell whether a relation is a function... SO DON'T SWEAT IT and enjoy your Sunday!!!
To answer your second question... more often than not a function will have a pattern of some sort, but a relation can have fairly random looking values and still be a function.
ReplyDeleteFor example:
(1,19),(3,-171),(5,-13.2) is a function
(1,2),(2,3),(2,4) is not a function because the input value of 2 is paired with two different numbers (3&4).
I kind of get it but I really don't understand it. What I have got from all of this is that a function basically determines another value, representing an input, correct??
ReplyDeleteYup... this is a tough concept... it takes awhile for "thinkers" to get this one to sink in. Don't worry too much, you have awhile before the quiz or test.
ReplyDeleteWe will go over it in class again and again each day... slowly but surely it will sink in... no need to memorize or stress... just come to class with an open mind... and keep re-reading the definition of a function each day and look at new examples... we'll get there, slow and steady wins this race!