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Grade Distribution 2nd 5th A 8 9 B 6 7 C 3 D 2 1 F 100+ Range 52-102
3 D 2 1 F No Shows 100+ Range 52-102 68-105 Avg 1/16/2019 4:23 PM 3.1 - Functions
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Pre-Calculus AB Pre-AP/Dual, Revised ©2015
Functions Section 3.1 Pre-Calculus AB Pre-AP/Dual, Revised ©2015 1/16/2019 4:23 PM 3.1 - Functions
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Key Terms Relation is a pairing of 2 items (like (x, y))
Domain is the X –values in a relation. Also known as INDEPENDENT Variable Range is the Y –values in a relation. Also known as DEPENDENT Variable “Y depends on X.” Function is a relation that for each domain element, there is only 1 range element. _X_ do not repeat. To determine the domain, Set the denominator EQUAL TO ZERO AND SOLVE. Those are your RESTRICTIONS You cannot take the square root of a negative number, or the nth root, where n is negative. Put the radicand equation GREATER TO EQUAL to zero. 1/16/2019 4:23 PM 3.1 - Functions
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Vertical Line Test Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function 1/16/2019 4:23 PM 3.1 - Functions
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YES Example 1 Would this graph be a function? 1/16/2019 4:23 PM
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NO Example 2 Would this graph be a function? 1/16/2019 4:23 PM
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NO Discontinuous at zero Example 3 Would this graph be a function?
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Example 4 Determine whether this function is defined as a function, y = x2 + 1? 1/16/2019 4:23 PM 3.1 - Functions
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Your Turn Determine whether this function is defined as a function, y2 = x2 + 1? 1/16/2019 4:23 PM 3.1 - Functions
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Example 5 1/16/2019 4:23 PM 3.1 - Functions
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Example 6 1/16/2019 4:23 PM 3.1 - Functions
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Example 7 1/16/2019 4:23 PM 3.1 - Functions
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Your Turn Determine whether the domain for the function, 𝒇 𝒙 = 𝒙 𝟐 (𝒙+𝟒)(𝒙−𝟏) in interval notation 1/16/2019 4:23 PM 3.1 - Functions
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Example 8 Given f (x) = x2 – 2x + 4, evaluate f (–5).
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Example 9 Given f (x) = x2 – 2x + 4, evaluate 𝒇 𝟐 1/16/2019 4:23 PM
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Example 10 Given f (x) = x2 – 2x + 4, evaluate f (x + 2).
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Your Turn Given g (x) = x2 + 4, evaluate g(a + 1). 1/16/2019 4:23 PM
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Difference Quotient A. Difference Quotient: 𝒇 𝒙+𝒉 −𝒇(𝒙) 𝒉
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Equation Difference Quotient: 1/16/2019 4:23 PM 3.1 - Functions
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Review If f (x) = 2x + 3, solve for f(5) If f (x) = 2x + 3, solve for f(a) If f (x) = 2x + 3, solve for f(x + h) 1/16/2019 4:23 PM 3.1 - Functions
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Example 11 Given f(x) = 5x – 6, use the Difference Quotient to simplify For every x, plug in a x For every x, plug in a x + h 1/16/2019 4:23 PM 3.1 - Functions
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Example 12 Given f(x) = 2x2 – 1, use the Difference Quotient to simplify 1/16/2019 4:23 PM 3.1 - Functions
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Your Turn Given f(x) = x2 – x + 2, use the Difference Quotient to simplify 1/16/2019 4:23 PM 3.1 - Functions
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Assignment Worksheet 1/16/2019 4:23 PM 3.1 - Functions
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