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Unit 1 Review

Unit 1 Review. 1. Relations and Intervals. Set-Builder Notation: {x | x>2} Interval Notation: (2, ∞) Relation: a set of ordered pairs Domain and Range: input and output Determine domains and ranges from graphs. Function: one to one relation

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Unit 1 Review

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  1. Unit 1 Review

  2. 1. Relations and Intervals • Set-Builder Notation: {x | x>2} • Interval Notation: (2, ∞) • Relation: a set of ordered pairs • Domain and Range: input and output Determine domains and ranges from graphs. • Function: one to one relation Independent variable, dependent variable, vertical line test

  3. Exercise • Which of the following representations may describe a function? A. A set of ordered pairs B. An equation C. A graph D. All of these

  4. 1. Linear Functions • General form: f(x) = ax + b • Zero of a function: f(x) = 0, x is the zero of the function • X-intercept: zero of a function • Y-intercept: value of y when x = 0 • Constant function: y = a • Domain, Range of a linear function

  5. 1. Linear Function • Slope: (y2-y1)/(x2-x1), rate of change • Geometric orientation based on slope • Slope of a vertical line: undefined • Slope-Intercept form: f(x) = mx+b • Point-slope form: y-y1 = m(x – x1) • Standard form: Ax + By = C, A ≠ 0

  6. 2. Linear Function • Two parallel lines: equal slopes • Perpendicular lines: m1×m2 = -1 • Linear Regression

  7. exercise • Skills test 1: #4 • Skills test 1: #8 • Skills test 1: # 10

  8. 3. Linear Equation and Inequalities • Addition and Multiplication Properties of Equality • Graphical approaches to solving linear equations: Intersection • X-intercept method: f(x) = g(x) , find the zero of F(x) = f(x)-g(x)

  9. 3. Linear Equation and Inequalities • Addition and multiplication properties of inequality • Graph approach: f(x) > g(x) • X-intercept method of solution of a linear inequality: F(x) >0, x such that F is above the x-axis • Three party Inequalities

  10. exercise • Exam review: # 6 • Exam review: # 8

  11. 4. Basic Function and Symmetry • Basic Functions and their domain & range ,get to know their corresponding graphs • Symmetry with respect to the y –axis: f(x) = f(-x), even function • Symmetry with respect to the x-axis: not a function, if (a,b) is on the graph, then (a, -b) is also on the graph • Symmetry with respect to the origin: f(x) = -f(-x), odd function

  12. exercise • Skills test 1: # 29 • Skills test 1: #30 • Exam review: #13 • Exam review: # 14

  13. 5. Transformations • Vertical and horizontal shift • Vertical and horizontal stretching and shrinking • Reflection • Basic rules: f(x) = cf(bx + a) + d order: b, a, c, d

  14. exercise • Exam review: #16 • Exam review: # 17

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