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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: If f = {(1,2), (2,-3), (3,1)} is a function, find 2+f
{(3,2),(4,-3), (5,1)}
{1,4), (2,-1), (3,1)}
{(2,4), (3,4), (3,5)}

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

Q 3: For f(x) = 2x, find f(5x)

Q 4: Given that f(x) = 2x and f: N->N, Check if f(2) + f(3) = f(2+3)

Q 5: Write the domain of the real function 10x

Q 6: State if f = {(1,2), (2,2), (3,2),(4,2)} is a function or not?

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Question 8: This question is available to subscribers only!

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