If the X,Y pair of coordinates is always some other value, then it is called as Algebric function. There are two terms used in algebraic function. They are Domain and Range. Domain is a set of all X values. Range is a set of all Y values.
A sample set of XY pairs of a function:
{ (2,4) , (3,6) , (4,8) }.
Let us see some more related terms in Algebric functions.
Example Problems on algebric function:
Problem 1:
Evaluate the algebric function: f(x) = 5x + 2 when x = 3.
Solution:
The given function is f(x) = 5x + 2
Substitute the x value in this given function.
f(3) = 5(3) + 2
= 15 + 2
f(3) = 17.
Therefore, f(x) = 17 when x = 3.
Problem 2:
Evaluate the algebric function: f(x) = x2 + x when x = -4.
Solution:
The given function is f(x) = x2 + x
Substitute the x value in this given function.
f(-4) = (-4)2 + (-4)
= 16 - 4
f(-4) = 12.
Therefore, f(x) = 12 when x = -4.
Problem 3:
Evaluate the algebric function: f(x) = x2 + 5x - 6 when x = 6.
Solution:
The given function is f(x) = x2 + 5x - 6
Substitute the x value in this given function.
f(6) = (6)2 + 5(6) - 6
= 36 + 30 - 6
f(6) = 60.
Therefore, f(x) = 60 when x = 6.
Other forms of algebric function:
The other types of algebraic functions are following.
Composite function:
Composite functions are a function in which we replace the output of one function and put it for the input of another function. The notation for composite functions are (f o g) (x) = f(g(x) , where the output of g(x) is used in the input of f(x).
Example:
Find (f o g) (x) = for the algebric function f(x) = x2 + 5x - 5 and g(x) = 4x + 3
Solution:
(f o g)(x) = f(g(x))
= f( 4x+3)
= (4x+3)2 + 5(4x+3) - 5
= (4x)2 + 24x + 32 + 20x + 15 - 5
= 16x2 + 24x + 9 + 20x + 10
= 16x2 + 44x + 19.
Linear and Quadratic function:
Linear function is a function where the highest power is always 1. The general form of linear function is f(x) = ax + b , where constants are a, b and a is not equal to 0.
Quadratic function is a function where the highest power is always 2. The general form of quadratic function is f(x) ax2 + bx + c ,where a and b, c are constants, and a is not 0.
Additional problems on i o functions algebra:
Example problem 3:
Find the value of f(1) for the function f(x) = -5x2 + x .
Solution:
The given function is f(x) =-5x2 + x.
Now, we have to find the value of f(1).
Substitute the value of x = 1 in the given function
f(1) = -5(1)2 + 1
f(1) = -5 + 1
f(1) = -4
So, the answer is f(1) = -4.
Example problem 4:
Find the ordered pairs of the function: f(x) = -5x + 4
Solution:
f(x)= -5x + 4
Substitute x=0
f (0) = -5(0) + 4
f(0) = 4
Therefore the ordered pair (x, f(0)) is (0, 4).
Substitute x = 1
f(1) = -5(1) + 4
f(1) = -1
Therefore the ordered pair (x, f(1)) is (1, -1).
Substitute x=2
f(2) = -5(2) + 4
f(2) = -6
Therefore the ordered pair (x, f(2)) is (2, -6).
Substitute x=3
f(3) = -5(3) + 4
f(3) = -11
Therefore the ordered pair (x, f(3)) is (3, -11).
The ordered pairs of the function f(x) = -5x + 4 is (0, 4), (1, -1), (2, -6), (3, -11).
Processing ...
No comments:
Post a Comment