Functions Relation Vertical Line Test Domain

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Presentation transcript:

Functions Relation Vertical Line Test Domain 1.2 Functions & Graphs Functions Relation Vertical Line Test Domain

Functions A function is a correspondence between a first set, called the domain, and a second set, call the range, such that each member of the domain corresponds to exactly one member of the range. Relation A relation is a correspondence between a first set, called the domain, and a second set, call the range, such that each member of the domain corresponds to at least one member of the range.

Does the following describe y as a function of x? The table below shows record low temperatures, in degrees Fahrenheit, in Orlando, FL Date in October, x 19 20 21 22 23 24 lowest temperature, y 52 65 69 72 67 58 The relationship between a student’s IQ x, and their SAT score, y. A person’s weight x, as a function of their height y. x (lbs) 125 200 110 107 132 y (in) 64 72 60 59.00 68 66

Does the table represent a function? Find the domain and range. Functions Let y = f(x) Does the table represent a function? Find the domain and range. What is the input when the output is -6? Find f(4) Find x such that f(x)=9. x 4 7 24 50 f(x) 9 12 -6 58 -19

Given f (x) = -3x+4, evaluate f (5a) f (a+1) Given 𝑓 (𝑥) = 2 − 𝑥 2 , evaluate f (a+2)

The graph of a function f is the set of all points on the plane of the form (x, f(x)). Vertical Line Test If it is possible for a vertical line to cross a graph more than once, then the graph is not the graph of a function.

Is this a function? Why? Is this a linear Function? Why? Find f(1). Find f(x) when x = 2. Find the inputs when the output is -2. Find the values of x for which f(x)=0. Domain? Range?

Domain - the set of all possible values of x (input) Domain - the set of all possible values of x (input). (Independent Variable) Range – the set of all possible values of y (output) (Dependent Variable) Domain Restrictions: Exclude any x-values that result in division by zero. Exclude any x-values that result in even roots of negative numbers Find Domain a. f(x) = 2x + 7 b. c. d. 𝑓(𝑥) = 1 𝑥+3

Is this a function? Why? Is this a linear Function? Why? x-intercepts? y-intercepts? Find f(-1) Find f(x) when x = -2. Find the inputs when the output is -5. Find the values of x for which f(x)=0. Domain? Range?