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

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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. 

a) The table below shows record low temperatures, in degrees Fahrenheit, in Orlando, FL

Does the following describe y as a function of x?

Date in October, x 19 20 21 22 23 24

lowest temperature, y 52 65 69 72 67 58

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b) The relationship between a student’s IQ x, and their SAT score, y.

c) A person’s weight x, as a function of their height y.

x (lbs) 125 200 110 107 200 132

y (in) 64 72 60 59.00 68 66

Functions

Let y = f(x)

a) Does the table represent a function?b) Find the domain and range.c) What is the input when the output is -6?d) Find f(4)e) Find x such that f(x)=9.

x 0 4 7 24 50f(x) 9 12 -6 58 -19

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Given f (x) = -3x+4, evaluatea) f (5a)

b) f (a+1)

Given , evaluatea) f (a+2)

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The graph of a function f is the set of all points on the plane of the form (x, f(x)).

Vertical Line TestIf it is possible for a vertical line to cross a graph more than once, then the graph is not the graph of a function.

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a) Is this a function? Why?b) Is this a linear Function?

Why?c) Find f(1).d) Find f(x) when x = 2.e) Find the inputs when the

output is -2. f) Find the values of x for

which f(x)=0.g) Domain?h) Range?

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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:1. Exclude any x-values that result in division by zero. 2. Exclude any x-values that result in even roots of negative numbers

Find Domain a. f(x) = 2x + 7 b.

c. d.

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42 8

yx

3 9y x

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a) Is this a function? Why?b) Is this a linear Function? Why?c) x-intercepts?d) y-intercepts?e) Find f(-1)f) Find f(x) when x = -2.g) Find the inputs when the output

is -5. h) Find the values of x for which

f(x)=0.i) Domain?j) Range?