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Pre-Calculus Chapter 1 Section 1 & 2

Pre-Calculus Chapter 1 Section 1 & 2. Modeling with Equations and Solving Functions and Their Properties 2013 - 2014.

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Pre-Calculus Chapter 1 Section 1 & 2

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  1. Pre-CalculusChapter 1Section 1 & 2 Modeling with Equations and Solving Functions and Their Properties 2013 - 2014

  2. A pizzeria sells a rectangular 20” by 22” pizza for the same amount as a large round pizza (24” diameter). If both pizzas are the same thickness, which option gives you the most pizza for the money

  3. The engineers at an auto manufacturer pay students $0.08 per mile plus $25 per day to road test their new vehicles. How much did the auto manufacturer pay Sally to drive 440 miles in one day? John earned $93 test-driving a new car in one day. How far did he drive?

  4. Things you should know about Functions • Domain: • Range: • Function: • Vertical Line Test: Input values, x, independent Output values, y, dependent Each domain value has 1 y value A graph is a function if a vertical line passes through it and only intercepts at 1 point

  5. Find the domain of the functions • , where A(s) is the area of an equilateral triangle with sides length s.

  6. Find the range of the function

  7. Continuity • Continuous • Removable discontinuity • Jump discontinuity • Infinite discontinuity

  8. Increasing and Decreasing Functions

  9. For each function, tell the intervals on which it is increasing and decreasing.

  10. Local and Absolute Extrema • Local values are located on an interval. Absolute values are the highest or lowest on the whole graph • Local maximum is the highest point in a section of a graph. If it is actually the highest point, it is the absolute maximum.

  11. Decide whether has any local maxima or local minima. If so, find each maximum or minimum value and the value of x at which it occurs.

  12. Symmetric about the y-axis For all x in the domain of f, These are even function.

  13. Symmetric about the x-axis These are not true functions because they fail the vertical line test. You can say (x, -y) is on the graph when (x, y) is on the graph.

  14. Symmetric about the origin For all x in the domain of f, This is called an odd function.

  15. Checking symmetry • To check if a function is an even function, subsitute (-x) in for x. If the function is the same, it is even. • To check if a function is odd, substitute (-x) in for x. If the function is the opposite sign of the original function, it is odd. • If the rules applied does not fit an even nor odd function, you would say the function is neither.

  16. Asymptotes • An asymptote is an imaginary line where the function does not exist. It can forever get closer to that line but will never actually touch the line.

  17. Finding Asymptotes • If a function is in fraction form, set the denominator equal to 0 to find vertical asymptotes. • Set the whole function equal to zero to find the horizontal asymptotes.

  18. Before you leave today: • Complete #79 from page 104

  19. Homework • Ch 1.1; Pg. 81-83: 1-10, 22, 29, 31 • Ch 1.2; Pg. 102-103: 1-25 every other odd, 41 – 61 every other odd, 73

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