Functions D2 Notes A
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This document contains 3 math problems asking to evaluate functions for given values: 1) Find f(3) for the function f(x) = 3x^2 - 4x, 2) Find g(-2) for the function g(x) = -x^2 + 5(x-2), 3) Find h(-2) for the function h(x) = |3x - 10| + 5x.
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This document contains 5 questions about evaluating various functions:
1) Find f(-8) and f(1) for the function f(x) = x + 8 + 2.
2) Find f(1) and f(-5) for the piecewise function f(x) = x^2 + 2 if x ≤ 1 and f(x) = 2x + 2 if x > 1.
3) Find all values of x such that f(x) = 0 for the function f(x) = 5x + 1.
4) Find the domain of the function h(t) = 4/t.
5) Find the value(s) of x for which
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1. The document discusses function notation, evaluating functions, and finding the domain from the equation of a function.
2. It provides examples of different types of function notation including f(x)=x^2+1 and {(x,y)|y=x^2+1}.
3. Evaluating a function involves substitution, and the document gives an example of evaluating f(x)=x^2+3x-1 when x=-2.
4. To find the domain from the equation, one looks at what type of equation it is such as linear, absolute value, quadratic, radical, fractional, or other. The domain is the set of inputs that can be substituted into the
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This study guide covers topics in precalculus including:
1) Examples of natural numbers, integers, rational numbers, and real numbers.
2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x).
3) Finding inverses of functions and verifying inverses by composition.
4) Operations on complex numbers including plotting, finding modulus, distance, midpoint, addition, subtraction, multiplication, and division.
5) Graphing functions, classifying function types, and stating domains and ranges.
6) Finding limits of functions as x approaches values.
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This document contains 5 questions about evaluating various functions:
1) Find f(-8) and f(1) for the function f(x) = x + 8 + 2.
2) Find f(1) and f(-5) for the piecewise function f(x) = x^2 + 2 if x ≤ 1 and f(x) = 2x + 2 if x > 1.
3) Find all values of x such that f(x) = 0 for the function f(x) = 5x + 1.
4) Find the domain of the function h(t) = 4/t.
5) Find the value(s) of x for which
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1. The document discusses function notation, evaluating functions, and finding the domain from the equation of a function.
2. It provides examples of different types of function notation including f(x)=x^2+1 and {(x,y)|y=x^2+1}.
3. Evaluating a function involves substitution, and the document gives an example of evaluating f(x)=x^2+3x-1 when x=-2.
4. To find the domain from the equation, one looks at what type of equation it is such as linear, absolute value, quadratic, radical, fractional, or other. The domain is the set of inputs that can be substituted into the
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This study guide covers topics in precalculus including:
1) Examples of natural numbers, integers, rational numbers, and real numbers.
2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x).
3) Finding inverses of functions and verifying inverses by composition.
4) Operations on complex numbers including plotting, finding modulus, distance, midpoint, addition, subtraction, multiplication, and division.
5) Graphing functions, classifying function types, and stating domains and ranges.
6) Finding limits of functions as x approaches values.
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The document discusses function composition and states some key rules: compositions are evaluated from the innermost function outwards; denominators cannot be zero and radicands cannot be negative. It provides examples of finding the compositions h(x) of various functions f(x) and g(x), and evaluating compositions like f(g(2)) at different values. The domain for compositions is also discussed.
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The document discusses five quadratic functions - f(x), g(x), h(x), j(x), and k(x) - and asks which are equivalent to the given function f(x) = -2x^2 + 4x + 16. It also provides another function f(x) = (5x - 10)(-4x + 20) and asks for its zeros and vertex. Finally, it gives a table representing a quadratic function and asks to write three equivalent functions that model the table.
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The document also provides examples of composite functions using flow diagrams to illustrate evaluating multiple simpler functions sequentially.
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This document provides examples of graphing composite functions. It explains that to find the domain of a composite function f(g(x)), you must consider the restrictions on the domains of both the inner and outer functions. It then gives three examples of determining the composite functions f(g(x)) and g(f(x)) for various functions f and g, and calculating or graphing their domains and ranges. The final example asks to determine possible functions f and g that satisfy three given composite functions.
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Day 2 Opener:
- Review problem solving linear equations from the previous day
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3.6 Notes A
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1.5 1.6 notes b
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1.5 1.6 notes b
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2.6 2.7 notes a
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2.4 notes b
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3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.