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High School Mathematics - 2
4.9 Functions

  1. A function is a relation (usually an equation) in which no two ordered pairs have the same x-coordinate when graphed.
  2. One way to tell if a graph is a function is the vertical line test, which says if it is possible for a vertical line to meet a graph more than once, the graph is not a function.
  3. Functions are usually denoted by letters such as f or g. If the first coordinate of an ordered pair is represented by x, the second coordinate (the y coordinate) can be represented by f(x).
  4. When a function is an equation, the domain is the set of numbers that are replacements for x that give a value for f(x) that is on the graph.

Example 1:
For f(x) = 2x+6, find f(5)
f(x) = 2x+6 = 2x5+6 = 10 + 6 = 16

Example 2:
Find the domain of the function f(x) = 4/x
x can take any value except zero. Since division by 0 is not defined.
Therefore, the domain is said to be x > 0 and x < 0.


Directions: Answer the following questions. Also write at least 10 examples of your own.
Q 1: State if f = {(1,2), (2,2), (3,2),(4,2)} is a function or not?
Yes
No

Q 2: Let X = {2,3} and Y = {1,3,5} , how many different functions are there from X into Y?
5
8
9

Q 3: Write the domain of the real function 10x
infinity
R
0

Q 4: For x>3, if f(x) = 3x -2 , g(x) = x2-2, find f3
(2x-1)
(3x-2)
(2x-1)3

Q 5: For f(x) = 2x, find f(5x)
5x
8x
10x

Q 6: Given that f(x) = 2x and f: N->N, Check if f(2) + f(3) = f(2+3)
no
yes

Q 7: For x>3, if f(x) = 3x -2 , g(x) = x2-2, find (3f - 2g)(x)
-2x2-6x+3
6x+2
-2x+3

Q 8: Let x = {2,3}, Y = {1,3,5}, ow many different functions are there from X into Y.
5
7
9

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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