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Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets:

Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets: Determine Whether a Relation Represents a Function Find the Value of a Function…plug it in, plug it in! Find the Domain if a Function…look at the x’s ! Identify the Graph of a Function

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Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets:

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  1. Coming after you with Ch. 2: Functions and Their Graphs • 2.1: Functions • Learning Targets: • Determine Whether a Relation Represents a Function • Find the Value of a Function…plug it in, plug it in! • Find the Domain if a Function…look at the x’s! • Identify the Graph of a Function • Obtain Information from the Graph of a Function

  2. Let X and Y be two nonempty sets of real numbers. A function from X into Y is a rule or a correspondence that associates with each element of X a unique element of Y. The set X is called the domain of the function. For each element x in X, the corresponding element y in Y is called the image of x. The set of all images of the elements of the domain is called the range of the function.

  3. f x y x y x X Y RANGE DOMAIN

  4. Determine which of the following relations represent functions. Not a function. Function. Function.

  5. Not a function. (2,1) and (2,-9)both work.

  6. Find the domain of the following functions: A) B) With a rational expression be sure to consider all values that may make it undefined.

  7. C) Even roots are real only for nonnegative numbers.

  8. Theorem: Vertical Line Test A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

  9. y x Not a function.

  10. y x Function.

  11. Determine the domain, range, and intercepts of the following graph. Find f(1). How often does the line y=-1 intersect the graph? For what value does f(x)=3? y 4 (2, 3) (10, 0) 0 (4, 0) (1, 0) x (0, -3) -4

  12. Finding values of a function For the function defined by f(x) = x2 - 2x, evaluate: (a) f(2) (b) f(x) + f(2) (c) f(x+2)(d) f(x+h) (a) f(2) = 22-2(2) = 0 (b) f(x) + f(2) = x2 - 2x + 0 (c) f(x+2) = (x+2)2 - 2(x + 2) = x2 + 4x + 4 - 2x - 4 = x2 + 2x (d) f(x+h) = (x + h)2 - 2(x + h) = x2 + 2xh + h2 - 2x - 2h

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