Brief Explanation of Function . Some algebraic functions

1. Function- Algebraic function
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2. What is function?
• https://www.geogebra.org/m/mzxvxe44
INPUT Num.
OUTPUT Num.
(INPUT, OUTPUT)
(3, 9), (4, 16)
Domain
Range
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Click here
f(x) = x2
Every input as a
unique output

3. -3
-2
-1
1
2
3
4
9
4
1
16
A B
f In arrow diagramA = {-3, - 2, - 1 ,1, 2, 3,4 }
f(x) = x2
https://www.geogebra.org/m/mzxvxe44
B = {9, 4 ,1, 16 }
Click here
In ordered pair form
f = { (- 3, 9), (- 2, 4), (- 1, 1), (1, 1), (2, 4), (3, 9), (4, 16) }
Domain
Range
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4. -3
-2
-1
1
2
3
4
9
4
1
16
2
A
B
fIn arrow diagram
In ordered pair form
f = { (- 3, 9), (- 2, 4), (- 1, 1), (1, 1), (2, 4), (3, 9), (4, 16) }
Domain
9
4
1
16
Range
Co-domain
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5. A relation from set A to a set B is said to
be a function if every elements of set A
has one and only one image in set B
What is function?
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6. Simple algebraic Functions
a. Linear Function
b. Constant function
c. Identity Function
d. Quadratic Function
e. Cubic Function
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7. a. Linear Function
A function is said to be a linear function if the polynomial is of
degree one.
Linear functions in the form of ax + by =c or y = mx + c
This types of the functions represents a straight lines
Example: x + y = 3
X 0 3 2
y 3 0 1
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8. b. Constant function: A function in the form of f(x) = c, where c is a
constant, is called a constant function.
It always represents a straight line which is parallel to X- AXIS
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9. Graph of Constant function
f(x) = c e.g f(x) = 3, y = 4, y = 5 , y = - 1
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It always represents a straight line which is parallel to X- AXIS

10. c. Identity Function
2
4
5
2
4
5
A B
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11. Identity function
A function in the form of f(x) = x is
called an identity function.
Example y = x , this is the function
from set A to B where A = {1, 3, 5, 7}
and B = {1, 3, 5, 7 }
• It maps every element into itself.
• Domain and range are same
• It represents a straight line bisecting
the angle between the axes of
coordinates( i.e X axis and Y- axis).
1
3
5
7
1
3
5
7
A
f
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12. • Example. For an identity function y = f(x ) = x
X 1 3 5 7
y 1 3 5 7
1
3
5
7
1
3
5
7
f
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13. Graph: Identity function y = f(x) = x
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14. d. Quadratic Function
• An algebraic function of second degree in the
form f(x) = ax2 + bx + c where a, b , c are real
numbers and a ≠ 0 is known as quadratic
function.
• Example : f(x) = x2 i.e. y = x2
The nature of the graph of the quadratic function is
called the parabola.
X -3 -2 -1 0 1 2 3 4
y 9 4 1 0 1 4 9 16
Parabola
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15. e. Cubic function
• An algebraic function of third degree
in the form of f(x) = ax3 + bx2 + cx + d,
a≠0 where a, b, c, d are real constant
is called a cubic function.
• Example: f(x) = 3x3+ 2, y = x3- 3x + etc.
• For the cubic function y = f(x) = x3, the
nature of the graph is shows below:
X 0 1 -1 2 -2
y 0 1 -1 8 -8
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