Math 8 lesson 3.2 (quarter 2)

1. Lesson 3.2
INDEPENDENT and
DEPENDENT VARIABLES,
DOMAIN and RANGE

2. REVIEW

3. REVIEW

4. Lesson 3.2
INDEPENDENT and
DEPENDENT VARIABLES,
DOMAIN and RANGE

5. Function Notation:
𝒚 = 𝒇(𝒙) 𝒚 = 𝟓𝒙 + 𝟐
𝒇(𝒙) = 𝟓𝒙 + 𝟐
Find 𝒇(𝟑) and
𝒇(−𝟏)

6. INDEPENDENT VARIABLE
 controls the dependent variable
DEPENDENT VARIABLE
 depends on the independent
variable

7. 1. Rosario is making souvenirs for
a friend’s wedding. The number of
invited people to attend the
wedding determines the number
of souvenirs she must make.

8. 2. George is selling
brownies online. The more
brownies he sells, the more
money
he earns.

9. 3. A bakery in Cabadbaran
City sells different types of
bread. The more bread the
customers buy, the more sacks
of flour they will use.

10. 4. During the school’s Mathematics
month celebration, the mathematics
teachers initiated different contests
categories and bought medals for the
winners. The more contests categories
there were in the celebration, the
more medals the teachers need to buy.

11. 5. Warren is going to take 2nd
Quarterly Exam. The number
of hours he spends studying
determines the score he will
get in the exam.

12. Domain
 set of all the first
coordinates
Range
 set of all the second
coordinates

13. Find the Domain and Range.
1. {(-3,4), (-2,5), (-1,5), (0,6)}
2.{(-3,2), (-2,5), (3,-1), (2,8)}
3. 4.

14. Find the Domain and Range.
5. 6.

15. Find the Domain and Range.
7. 8.

16. Find the Domain and Range.
9. 10.

17. Find the Domain and Range.
11. 𝒚 = 𝒙 + 𝟑
12. 𝒚 = 𝟐𝒙 − 𝟔
13. 𝒚 =
𝟐
𝒙−𝟐

18. RESTRICTIONS
1. Radicals with even indices
Radicands must be nonnegative
2. Fractions
Denominator should not be zero

19. Find the Domain and Range.
11. 𝒚 = 𝒙 + 𝟑
1. Radicals with even
indices
Radicands must be
nonnegative
2. Fractions
Denominator should not
be zero
No radical sign
in the
variable and no
variable in the
denominator so
D: 𝒙 𝒙 ∈ ℝ
For the range we need to find first
the inverse of the function.
𝒚 = 𝒙 + 𝟑 Given
𝒙 = 𝒚 + 𝟑 Interchange x and y
−𝒚 = −𝒙 + 𝟑
solve for y in terms of x
−𝟏 − 𝟏
𝒚 = 𝒙 − 𝟑
No radical sign in the
variable and no variable in
the denominator so
R: 𝒚 𝒚 ∈ ℝ
 inverse

20. Find the Domain and Range.
12. 𝒚 = 𝟐𝒙 − 𝟔
1. Radicals with even
indices
Radicands must be
nonnegative
2. Fractions
Denominator should not
be zero
There is a radical sign so
radicand
𝟐𝒙 − 𝟔 ≥ 𝟎 nonnegative
Solve for x
𝟐𝒙 ≥ 𝟔
𝟐 𝟐
𝒙 ≥ 𝟑
D: 𝒙 𝒙 ≥ 𝟑
For the range we need to find first
the inverse of the function.
𝒚 = 𝟐𝒙 − 𝟔 Given
𝒙 = 𝟐𝒚 − 𝟔
Interchange x and y
solve for y in terms of x
𝟐
𝒙𝟐 = 𝟐𝒚 − 𝟔
−𝟐𝒚 = −𝒙𝟐
− 𝟔
−𝟐 −𝟐
𝒚 =
𝟏
𝟐
𝒙𝟐 + 𝟑
No radical sign in the
variable and no variable in
the denominator so
R: 𝒚 𝒚 ∈ ℝ
Inverse

21. Find the Domain and Range.
13. 𝒚 =
𝟐
𝒙−𝟐
1. Radicals with even
indices
Radicands must be
nonnegative
2. Fractions
Denominator should not
be zero
𝒙 − 𝟐 ≠ 𝟎
Solve for x
𝒙 ≠ 𝟐
D: 𝒙 𝒙 ≠ 𝟐
For the range we need to find first the inverse of
the function.
𝒚 =
𝟐
𝒙 − 𝟐
Given
𝒙 =
𝟐
𝒚 − 𝟐
Interchange x
and y
solve for y in
terms of x
𝒚 − 𝟐 𝒚 − 𝟐
𝒙𝒚 − 𝟐𝒙 = 𝟐
𝒙𝒚 = 𝟐𝒙 + 𝟐
𝒙 𝒙
𝒚 =
𝟐𝒙 + 𝟐
𝒙
Inverse
𝒙 ≠ 𝟎
R: 𝒚 𝒚 ≠ 𝟎

22. ACTIVITY #3: Find the Domain and Range.

23. ACTIVITY #3: Find the Domain and Range.
9. 𝒚 = 𝟑𝒙 − 𝟗