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Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Functions
Section 2.4/2.5
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Questions? –Spiral #1 is Tuesday!
•Fractions•Sign Rules•Multiply Polynomials
•Solve Equations•Simplify Radicals
•Classify Numbers•Tell Properties
•Use Order of Operations
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Definitions
•Relation –2 paired variables
•Function –relationship such that for every x there is only one y
•Domain –All possible xvalues
•Range –All possible yvalues
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range.
{(3, 5), (4, 8), (5, 6), (7, 10), (8, 2)}
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range.
{(5, 8), (6, 7), (3, 1), (4, 2), (5, 9), (12, 2)}
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range.
{(2, 3), (4, 6), (3, 1), (7, 6), (9, 3), (2, 8)}
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range .
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Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range.
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Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a function? Give the domain and range.
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Day 2 Introduction to Functions with notes.notebook
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Interval Notation
NotationMeaningGraph(1, 4){x| 1< x < 4}
[1, 4]{x| 1 ≤ x ≤ 4}
(1, 4]{x| 1 < x ≤ 4}
[1, ∞){x | x ≥ 1}
( ∞, 4){x | x < 4}
( ∞ , ∞) ℝ, set of all real numbers.
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Vertical Line Test
•Used to determine if a graph is a function.
•If a vertical line intersects the graph at more than 1 point, then the graph is not a function.
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a Function? Give the domain & Range
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a Function? Give the domain & range
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a Function? Give the domain & range.
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Is it a Function? Give the domain & range.
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Inverse of a relation
•Of the ordered pairs (x, y) is the set of all ordered pairs (y, x).
•Domain of the inverse is the range of the original.
•Range of the inverse is the domain of the original.
•Symbol: f (x)-1
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Example: {(1,2), (2, 4), (3, 6), (4, 8)}
Inverse:
Day 2 Introduction to Functions with notes.notebook
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Draw the inverse. Compare to the line y = x.
Day 2 Introduction to Functions with notes.notebook
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August 28, 2012
Draw the inverse. Compare to the line y = x.
Day 2 Introduction to Functions with notes.notebook
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So how can I look at the graph of a function and decide if its inverse is also going to be a
function?
Day 2 Introduction to Functions with notes.notebook
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Homework
•Worksheet
