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### High School Mathematics - 24.13 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: State if f = {(1,2), (2,2), (3,2),(4,2)} is a function or not? write Y or NAnswer: Q 2: If f = {(1,2), (2,-3), (3,1)} is a function, find 2+fAnswer: Q 3: f: R -> R be defined by f(x) = 10x - 7. if g = f-1 then g(x) is Answer: Q 4: Let x = {2,3}, Y = {1,3,5}, how many different functions are there from X into Y.Answer: Q 5: Draw the graph of the function f: R-> R defined by f(x) = |x| Answer: Q 6: Given f(x) = 3 , g(x) = 5y, find f(x).g(x).Answer: Q 7: For f(x) = 2x, find f(5x)Answer: Q 8: If f: R ->R be defined by f(x) = 3x- 4, then f-1(x) is Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!