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High School Mathematics - 2
4.13 Functions - Review

  • Constant functions: Functions that stay the same no matter what the variable does are called constant functions.
  • Constants: are things that do not change: for example distance, volume, mass, are called constants. The things that do change are called variables
  • Continuous graph: In a graph, a continuous line with no breaks in it forms a continuous graph
  • Discontinuous graph: A line in a graph that is interrupted, or has breaks in it forms a discontinuous graph
  • Function: A function f of a variable x is a rule that assigns to each number x in the function's domain a single number f(x). The word "single" in this definition is very important graph A visual representation of data that displays the relationship among variables, usually cast along x and y axes.
  • Relation: A relation is any pairing of a set of inputs with a set of outputs. Every function is a relation, but not every relation is a function. A relation is a function if for every input there is exactly one output.
  • Mapping
  • Input: The number or value that is entered, for example, into a function machine. The number that goes into the machine is the input
  • Origin In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero (0,0)
  • Output: The number or value that comes out from a process. For example, in a function machine, a number goes in, something is done to it, and the resulting number is the output
  • Domain
  • Range
  • Vertical line test: A relation represented by a graph is a function provided that no vertical line passes through more than one point on the graph.
  • Test for Functions: Vertical Line test.
  • Kinds of Mapping: one to one, many to one, onto, and into function.
  • one to many and many to many are not functions.
  • Type of Functions:
    • Linear functions
    • Linear functions
    • Absolute Value functions
    • Absolute Value In-equation functions
    • Quadratic functions
    • Rational functions
    • Radical functions
    • Inverse functions
    • Exponential Functions
    • Logarithmic functions
    • Polynomial functions
    • Trigonometric functions

Q 1: Given f(x) = 3 , g(x) = 5y, find f(x).g(x).

Q 2: f: R -> R be defined by f(x) = 10x - 7. if g = f-1 then g(x) is

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

Q 4: Given f(x) = 3x - 2, find f(x-3).

Q 5: If f: x -> 2x, g: x -> x2 and h: x -> x +1. Find the formula for ho(gof)

Q 6: Let x = {2,3}, Y = {1,3,5}, how many different functions are there from X into Y.

Q 7: If f: R ->R be defined by f(x) = 3x- 4, then f-1(x) is

Q 8: If f = {(1,2), (2,-3), (3,1)} is a function, find 2+f

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Question 10: This question is available to subscribers only!

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