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Approaches to Mathematics: Graphs and Models

Learn different approaches to mathematics, including verbal explanations, numerical tables, graphical representations, and analytical manipulation of symbols and equations. Explore methods for sketching graphs, calculating zeros, finding intercepts, and identifying symmetry. Gain a deeper understanding of mathematical concepts without relying solely on a graphing calculator.

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Approaches to Mathematics: Graphs and Models

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  1. Warm-Up Explain how you made each match (Without a calculator!)

  2. Section P.1: Graphs and Models p.3 - 10

  3. 4 Approaches to Mathematics: • Verbal – Explain in words • Numerical – Table of values • Graphical – Using graphs • Analytical – Manipulating symbols and equations

  4. Sketch a graph of f(x) = 1 – x2 Method 1: Make a table and plot points.

  5. Sketch a graph of f(x) = 1 – x2 Method 2: Using a graphing calculator.

  6. Why not just always use a graphing calculator? • Give the number of zeros of f(x) = sin(ln x)

  7. Why not always just use a graphing calculator? • Graph y =

  8. Finding x and y-intercepts: x2y – x2 + 4y = 0

  9. Finding x and y-intercepts: • y =

  10. Symmetry: • X-axis: • Y-axis: • Origin:

  11. Check for symmetry: y = (x + 2)2

  12. Why does symmetry help? x – y2 = 2

  13. Find Points of Intersection and check: • x2 + y = 5 x – y = 1

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