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Published byScott McGee Modified over 9 years ago
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We saw yesterday that every relationship between x- and y-values represent a relation. That means every graph on a coordinate grid represents a relation
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How can we write this relation down? As ordered pairs, a table, or a mapping diagram. {(1,5),(3,5),(4,2),(6,-2)} Is it a function?
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How can we write this relation down? We cannot write every point on this graph down – there is always another in between so the only way is to write an equation. y = 2x + 4 Is this a function?
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D: {1,3,4,6} R: {-2,2,5}
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D: x can be anything R: y can be anything A better way is to use set notation
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To use the symbols of algebra, we could write the domain as Does that look like a foreign language? Let’s translate:
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The curly braces just tell us we have a set of numbers.
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The x reminds us that our set contains x-values.
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The colon says, such that
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The symbol that looks like an e (or a c sticking its tongue out) says, belongs to or is an element of...
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And the cursive, or script, R is short for the set of real numbers.
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R, the set So we read it, “The set of xsuch that x belongs to of real numbers.”
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“The set of y, such that y belongs to R, the set of real numbers.” Read this:
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the domain and range can be any real number. It is not always true that Sometimes mathematicians want to study a function over a limited domain.
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What do you think of the domain? What about the range?
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What do you think of the domain? What about the range? Function or not?
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What do you think of the domain? What about the range? Function or not?
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HW Worksheet Domain and Range
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When we know that a relation is a function, the “y” in the equation can be replaced with f(x). f(x) is simply a notation to designate a function. It is pronounced ‘f’ of ‘x’. The ‘f’ names the function, the ‘x’ tells the variable that is being used.
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Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2. Find f(4): f(4) = 4 - 2 f(4) = 2
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If g(s) = 2s + 3, find g(-2). g(-2) = 2(-2) + 3 =-4 + 3 = -1 g(-2) = -1
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If h(x) = x 2 - x + 7, find h(2c). h(2c) = (2c) 2 – (2c) + 7 = 4c 2 - 2c + 7
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If f(k) = k 2 - 3, find f(a - 1) f(a - 1)=(a - 1) 2 - 3 (Remember FOIL?!) =(a-1)(a-1) - 3 = a 2 - a - a + 1 - 3 = a 2 - 2a - 2
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pg 635 #2, 4, 6, 8 (no sketch)
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Solve the equation for y. Substitute any value for x and find how many answers it produces for y. One: function More than one: not a function 2x + 4y = 8 y = -0.5x + 2 This equation produces one output for every input so it is a function
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This equation will produce two outputs for every input and is therefore not a function
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If and find:
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If and find:
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If and find:
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Worksheet
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Finding and Graphing
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