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Graphs & Models (P1)

Graphs & Models (P1). September 5th, 2012. I. The Graph of an Equation. Ex. 1 : Sketch the graph of y = (x - 1) 2 - 3. You try: Sketch the graph of a. y = (x + 3) 2 + 4 b. y = (x - 2) 2 - 1 c. y = -(x + 1) 2 + 3. Ex. 2 : Use a graphing utility to graph each equation.

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Graphs & Models (P1)

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  1. Graphs & Models (P1) • September 5th, 2012

  2. I. The Graph of an Equation • Ex. 1: Sketch the graph of y = (x - 1)2 - 3.

  3. You try: Sketch the graph of a. y = (x + 3)2 + 4 b. y = (x - 2)2 - 1 c. y = -(x + 1)2 + 3

  4. Ex. 2: Use a graphing utility to graph each equation. • a. y = x3 - 3x2 + 2x + 5 • b. y = x3 - 3x2 + 2x + 25 • c. y = -x3 - 3x2 + 20x + 5 • d. y = 3x3 - 40x2 + 50x - 45 • e. y = -(x + 12)3 • f. y = (x - 2)(x - 4)(x - 6)

  5. II. Intercepts of a Graph Def: The x-intercept of a graph is the point (a, 0) where the graph crosses the x-axis. Find it by plugging y = 0 into the equation and solving for x. The y-intercept is the point (0, b) where the graph crosses the y-axis. Find it by plugging x = 0 into the equation and solving for y.

  6. Ex. 3: Find the x- and y-intercepts of the graph of y = x3 - 5x2 - 6x.

  7. You try: Find the x- and y-intercepts of the graph of y = 9x4 - 25x2.

  8. Ex. 4: Use a graphing utility to find the x- and y-intercepts of the graph of y = x4 - 3x3 + 2x2 - x - 4.

  9. III. Symmetry of a Graph Tests for Symmetry: 1. y-axis: Replacing (x, y) with (-x, y) yields an equivalent equation.

  10. 2. x-axis: Replacing (x, y) with (x, -y) yields an equivalent equation.

  11. 3. origin: Replacing (x, y) with (-x, -y) yields an equivalent equation.

  12. Ex. 5: Test the graph of the equation y = x3 - 4x for symmetry with respect to each axis and the origin.

  13. You try: Sketch the graph of the equation 2x + y2 = 4. Identify any intercepts and test for symmetry.

  14. IV. Points of Intersection Ex. 6: Find the points of intersection of the graphs of the equations x + 3y = -2 and x2 - y = 4.

  15. You try: Find the points of intersection of the graphs of the equations x = y - 2 and x2 + y2 = 10.

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