Relation and Function

1. Domain and
Range

2. The domain of a function f is the set of values
of x for which f is defined.
Domain
The range of a function f is the set of values
of f(x), where x is an element of the domain
of f.
Range

3. Which of the following given describes a
function? Find its domain and range.
A={(0,1),(1,2),(2,3),(3,4),(4,5)}
B={(4,2),(-3,2),(-4,2),(5,2),(-5,2)}
C={(-1,2),(-3,-3),(-4,5),(-5,-5),(-5,7)}
Learning Task 1
Function
D: {0,1,2,3,4}
R: {1,2,3,4,5}
Function
D: {4,-3,-4,5,-5}
R: {2}
Not Function
D: {-1,-3,-4,-5}
R: {2,-3,5,-5,7}

4. Give range of the following if the domain is
{-2,0,2,4}
1. y=-x+3
Learning Task 2
when x=-2
y=-(-2)+3
=2+3
y=5
when x=0
y=-(0)+3
=0+3
y=3
when x=2
y=-(2)+3
=-2+3
y=1
when x=4
y=-(4)+3
=-4+3
y=-1
Solution:
Thus, R:{5,3,1,-1}.

5. 2. y=2x
when x=-2
y=2(-2)
y=-4
when x=0
y=2(0)
y=0
when x=2
y=2(2)
y=4
when x=4
y=2(4)
y=8
Solution:
Thus, R:{-4,0,4,8}.

6. Find f(x) for a given value of x by substituting the value x into
the equation. The domain is the of all x-values that makes
sense in the equation.
x- values function-values,
f(x) = -3x + 5
x = 2
x = 3
x = 4
x = 5
f(2) = -3(2) + 5 = -1
f(3) = -3(3) + 5 = -4
f(4) = -3(4) + 5 = -7
f(5) = -3(5) + 5 = -10
Learning Task 3

7. Learning Task 4
Find its domain and range of the function given
equation.
A. 𝒇 𝒙 = 𝟓𝒙 + 𝟑
B. 𝒇 𝒙 = 𝟖𝒙 + 𝟏
C. 𝒇 𝒙 = −𝒙 + 𝟐
D. 𝒇 𝒙 = 𝟗𝒙 + 𝟓
Domain: 𝒙|𝒙 ∈ 𝑹
Range: 𝒚|𝒚 ∈ 𝑹

8. Find its domain and range of the function given
equation.
E. 𝒇 𝒙 = 𝒙𝟐
+ 𝟑
F. 𝒇 𝒙 = −𝟑𝒙𝟐
− 𝟕
Domain: 𝒙|𝒙 ∈ 𝑹
Range: 𝒚|𝒚 ≥ 𝟑
Domain: 𝒙|𝒙 ∈ 𝑹
Range: 𝒚|𝒚 ≤ −𝟕

9. Find its domain and range of the function given
equation.
G. 𝒇 𝒙 = 𝒙
F. 𝒇 𝒙 = 𝒙 + 𝟓
Domain: 𝒙|𝒙 ≥ 𝟎
Range: 𝒚|𝒚 ∈ 𝑹
Domain: 𝒙|𝒙 ≥ −𝟓
Range: 𝒚|𝒚 ∈ 𝑹

10. Find its domain and range of the function given
equation.
G. 𝒇 𝒙 =
𝟑
𝒙
F. 𝒇 𝒙 =
𝟓
𝒙+𝟐
Domain: 𝒙|𝒙 ∈ 𝑹, 𝒙 ≠ 𝟎
Range: 𝒚|𝒚 ∈ 𝑹, 𝒙 ≠ 𝟎
Domain: 𝒙|𝒙 ∈ 𝑹, 𝒙 ≠ −𝟐
Range: 𝒚|𝒚 ∈ 𝑹, 𝒚 ≠ 𝟎

11. Find the domain and range of each graph.
Learning Task 5

12. Extends on
both direction

13. (3,1)
Extends on
both direction

14. PROBLEM
SOLVING

16. Therefore, the estimated bus fare from Imus City to Tagaytay City
is P32.70.

17. Thank you for listening ☺