1.5 I understand Functions. Function For each input there is only one output Ex: Let g represent the...
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Transcript of 1.5 I understand Functions. Function For each input there is only one output Ex: Let g represent the...
![Page 1: 1.5 I understand Functions. Function For each input there is only one output Ex: Let g represent the age of a US citizen and d represent the number of.](https://reader030.fdocuments.net/reader030/viewer/2022033107/56649d755503460f94a55f27/html5/thumbnails/1.jpg)
1.5 I understand Functions
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Function
• For each input there is only one output• Ex: Let g represent the age of a US citizen and
d represent the number of days since his or her birth. Is g a function of d or is d a function of g?
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If y is a function of x
• Independent variable: x • Dependent variable: y
• The DETERMINES the value of .
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Relation
• A set of ordered pairs• Can be indicated by a verbal description, a
graph, a formula or equation, or a table• Not every relation is a function, but every
function is a relation.
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Determine if each relation is a function:
•
X Y
1 9
20 29
6 10
-1 9
X Y
5 7
6 8
7 9
5 6
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Vertical Line Test
• A graph is a function if and only if there is no vertical line that crosses the graph more than once
• AKA: When you draw a vertical line on the graph, if it intersects with the graph more than once, it is NOT a function
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Use the Vertical Line Test to determine if the graph is a function
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Identifying a function from an equation
•
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Domain and Range
•
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Determine the Domain and Range (Put into calculators if needed)
•
12 xy
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Function Notation
• A function defined by a set of ordered pairs can be named with a letter
= { (2,5), (3,8)}Since pairs 2 with 5, we write f(2)=5The value at 2 is 5.f(3)=8; The value at 3 is 8.
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Using Function Notation
• 3)( xxf
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Using Function Notation with Variables
• 2)( 2 xxf
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The Average Rate of Change
• Slope =
• It is not necessary to have a formula for a function to find the average rate of change, you can find the average rate of change (slope) if you know two points on the graph.
12
12
xx
yy
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Average Rate of Change (slope)
• Find the average rate of change between the two points.
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Example 1
• The population of California was 29.8 million in 1990 and 33.9 million in 2000. What was the average rate of change of the population over that time interval?
• Use the coordiantes (year, population) (1990, 29,800,000) and (2000, 33,900,000)
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The Difference Quotient
h
xfhxf )()(
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Find and simplify the difference quotient
•
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Find and simplify the difference quotient
•
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Find and simplify the difference quotient
xxf )(
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1.6 Graphs of Relations and Functions
• Parent Functions• Graph the following parent functions and
state the domain and range.
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X Y
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X Y
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X Y
The Absolute Value Function
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The square root function:
xy
xy
X Y
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The Cubic function:
X Y
3xy
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X Y
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X Y
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X Y
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X Y