Алматы «Сүлейман Демирел атындағы мектеп-интернат-колледж»
2021 – 2022 жж.
Open lesson
Lesson : Algebra
Topic : The function. The graph of a function.
Class : 7A, 7B, 7C
Term : II
Date : 16.11.2021 - 20.11.2021 (1st week)
Time : 45 min
Aims : acquaintance with a new topic and learn graphing
There are many variables around us. Some of them are closely related to each other and some of them are not. For
instance, the number of students in a classroom and the quantity of oxygen in the same classroom are closely
related. But the number of students in a classroom and the temperature outside are not related at all. Functions are
used to show this relation between variables. Using that relation we can estimate the results for possible cases.
Definition: A function f is a rule that assigns to each element x in set A exactly one element y or f(x)
in set B. Set A is called the domain and set B is called the range of the function f. We name
x as the independent variable or the argument, and y as the dependent variable since the
value of y depends on x.
Example 1: State whether the following relations define a function or not.
a. {(0, 2), (0, 3), (1, 6), (2, 4), (3, 5)}
b. {(–3, 1), (–1, –1), (0, 1), (1, 3), (2, –2)}
c. A set of ordered pairs of the form (radius, area of circle)
d. A set of ordered pairs of the form (name, surname)
e. {(1, z), (2, d), (4, f)} with the domain {1, 2, 3, 4}
Solution:
a. In order to have a function for each value in the domain we should have exactly one element assigned in
the range. Since 0 is assigned both to 2 and 3, this is not a function.
b. The domain is {–3, –1, 0, 1, 2}. Since there is only one value assigned for each value in the domain, this is
a function. Note that in the image on the right –3 and 0 are both assigned to 1, but this does not prevent it
from being a function. The elements from the domain may be assigned to the same value from the range.
The important point is that each element of the domain must not have more than one different value from
the range.
c. For each given radius there is exactly one possible circle area. This relation is a function.
d. Two people with the same name can have different surnames. This relation is not a function.
e. As in the previous examples if nothing else is stated as the domain, the set of all the first components is
the domain. For this example it would be obvious to think that the domain is {1, 2, 4}. This relation is a
function if we didn't see the phrase “with domain {1, 2, 3, 4}”. But the definition of a function states that
every element in a domain must be assigned by exactly one element. We can see that the element “3” from
the domain remains unassigned. Therefore this relation is not a function.
Teacher: Dias Beimbetov
Алматы «Сүлейман Демирел атындағы мектеп-интернат-колледж»
2021 – 2022 жж.
Class Work:
Home Work:
Give exercises for self-study and mark from CW#1 – Worksheet
on https://almatyboysbilim.edupage.org “7th grade Algebra” HW#1 – Worksheet
Teacher: Dias Beimbetov