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Warm-up: Copy Quiz Topics Linear Equations + word problems Circle equation

HW 1.4: Pg. 48-50 #9, 30, 31, 35, 57-69 odd Quiz next class!. September 12, 2012 - Determine whether relationships between two variables are functions - Use function notation and evaluate functions - Find the domains of functions. Warm-up: Copy Quiz Topics Linear Equations + word problems

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Warm-up: Copy Quiz Topics Linear Equations + word problems Circle equation

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  1. HW 1.4: Pg. 48-50 #9, 30, 31, 35, 57-69 odd Quiz next class! September 12, 2012- Determine whether relationships between two variables are functions- Use function notation and evaluate functions- Find the domains of functions Warm-up: Copy Quiz Topics Linear Equations + word problems Circle equation x- and y-intercepts Symmetry Functions – evaluating

  2. Check 1.2-1.3 Word Problems Pg. 23 #72 Compare graphs Pg. 36 #96 a) Largest increase 2002-03; least increase 2000-2001 b) slope from 94-2003 = 9.18 c) #106 y(t) = -749.5t + 10,821.5; y(18) = -2669.5; y(20) = -4168.5 #109 a) y(t) = 179.5t + 40,571; b) y(8) = 42,007; y(10) = 42,366; c) m = 179.5

  3. Lesson 1.4 Functions A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain (or set of inputs) of the function f, and the set B contains the range (or set of outputs).

  4. Four Ways to Represent a Function “The input value x is the number of representatives from a state, and the output value of y is the number of senators.” • Verbally • Numerically • Graphically • Algebraically (2, 11), (2, 10), (3, 8), (4, 5) y = x2 + 2x + 1

  5. Function Notation f(x) Ex 1) Evaluating a function g(x) = -x2 + 4x + 1 Find the function value for the following: a) g(2) b) g(t) c) g(x + 2) Replace all the x’s with the value of 2 g(t) = -(t)2 + 4(t) + 1 g(x +2) = -(x+2)2 + 4(x + 2) + 1 g(2) = -(2)2 + 4(2) + 1 g(t) = -t2 + 4t + 1 g(x + 2) = -(x+2)(x+2) + 4(x + 2) + 1 g(2) = -4+ 8 + 1 g(x + 2) = -(x2 + 4x + 4)+ 4(x + 2) + 1 g(2) = 5 g(x + 2) = -x2 - 4x - 4+ 4x + 8 + 1 g(x +2) = -x2 + 5

  6. Evaluating a piecewise-defined function (two or more equations over a specified domain) Example 2) Evaluate the function when x = -1, 0, and 1 • It gives you two conditions: • Use x2 + 1, if x < 0 • Use x – 1, x ≥ 0 f(-1) = (-1)2 + 1 f(0) = 0 – 1 f(1) = 1 – 1 f(-1) = 1 + 1 f(0) = – 1 f(1) = 0 f(-1) = 2

  7. Practice • Evaluate f(x) = x2 + 1 for: a) f(-4) b) f(t2) c) f(t + 1) • Evaluate for: a) f(-2) b) f(-1) c) f(0) 17 t4 + 1 t2 + 2t + 2 -3 -1 1

  8. Finding the Domain of a Function There are exceptions to what values can be inputted into a function. For example: A fraction A square root Quadratic {x| x ≥ 0} {x| x is all real numbers} {x| x is all real numbers, x ≠ 0} Graphing the function also helps you see the domain.

  9. PracticeFind the domain for each function 3. 4. 5.

  10. Evaluating a Difference QuotientThe difference quotient is the slope of the secant line that goes through two points of a function. This slope is very important in calculus where it is used to define the derivative of function f. Evaluate f(x) = x2 – 4x + 7 Answer 2x + h – 4

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