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PreCalculus M 117 A

PreCalculus M 117 A. Contemporary Precalculus, 3rd edtion - Thomas W. Hungerford Br. Joel Baumeyer, F.S.C. Christian Brothers University. Distance Formula. The distance between points (x 1 ,y 1 ) and (x 2 ,y 2 ) is: The equation of a circle is:

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PreCalculus M 117 A

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  1. PreCalculus M 117 A • Contemporary Precalculus, 3rd edtion • - Thomas W. Hungerford • Br. Joel Baumeyer, F.S.C. • Christian Brothers University

  2. Distance Formula • The distance between points (x1,y1) and (x2,y2) is: • The equation of a circle is: where (h,k) is the center and r is the radius.

  3. Basic Principles for Solving Equations • If the product of two real numbers is zero, then at least one of them is zero, i.e. if ab = 0, either a, b or both are zero. • Linear: ax + b = c • Get the variable by itself on one side of the equation by • 1. Add or subtracct the same quantity from both sides of the equation • 2. Multiply or divide both sides of the equation by the same non-zero quantity

  4. Basic Principles for Solving Equations (con’d) • Quadratic: ax2 + bx + c = 0 • Get the equation into the form above. • Then

  5. Steps in Solving Word Problems

  6. Working Definition of Function: H = f(t) • A function is a rule (equation) which assigns to each element of the domain (x value or independent variable) one and only one element of the range (y value or dependent variable). • Domain is the set of all possible values of the independent variable (x). • Range is the corresponding set of values of the dependent variable (y).

  7. General Types of Functions(Examples): • Linear: y = m(x) + b; proportion: y = kx • Polynomial: Quadratic: y =x2 ; Cubic: y= x3 ; etc • Power Functions: y = kxp • Trigonometric: y = sin x, y = Arctan x • Exponential: y = aebx ; Logarithmic: y = ln x

  8. Graph of a Function: • The graph of a function is all the points in the Cartesian plane whose coordinates make the rule (equation) of the function a true statement.

  9. Slope • m - slope : b: y-intercept • a: x-intercept • .

  10. 5 Forms of the Linear Equation • Slope-intercept: y = f(x) = b + mx • Slope-point: • Two point: • Two intercept: • General Form: Ax + By = C

  11. Basic Facts for Straight Lines and Their Slopes • If two lines have the same slope, they are parallel; i.e. m1 = m2 • Two lines are perpendicular if the product of their slopes is -1; i.e. m1m2 = -1 • A horizontal line has a slope of 0 and has an equation of the form: y = b. • A vertical line has an undefined slope and an equation of the form: x = c.

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