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Bell Assignment

Bell Assignment. Graph the equation y = x 3 + 3x 2 – 1 on your GUT. Then use the graph to describe the increasing or decreasing behavior of the function. Graph the following equation. f(x) = -½x – 6 ; x ≤ -4 x + 5 ; x > -4.

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Bell Assignment

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  1. Bell Assignment • Graph the equation y = x3 + 3x2 – 1 on your GUT. Then use the graph to describe the increasing or decreasing behavior of the function. • Graph the following equation. f(x) = -½x – 6 ; x ≤ -4 x + 5 ; x > -4

  2. 1.4 Shifting, Reflecting, and Stretching Graphs

  3. Ways to write functions: In Algebra 2: y = x2 + 3 y = (x+3)2 y = 3x2 In Pre-Cal h(x) = f(x) + 3 g(x) = f(x + 3) q(x) = 3 f(x) f(x) = x2 y = x2 Original Function

  4. Ways to write functions: In Algebra 2: y = x – 2 y = x -2 y = ½ x In Pre – Cal h(x) = f(x) – 2 p(x) = f(x – 2) q(x) = ½ f(x) y = x f(x)= x

  5. Shifting and Reflecting Graphs Label Points: Notice (x, y) (-x, y) Over _____ (x, y) (x, -y) Over _____ y axis x axis so f(-x) reflects over the y axis because you negate the x value. -f(x) reflects over the x axis because you negate the y value.

  6. f(-x) means to negate the x value and therefore reflects over the y axis. -f(x) means to negate the y value and therefore reflects over the x axis.

  7. Compare the graph of each function with the graph of f(x) = x3 In Words: In Terms of f(x) g(x) = x3 – 1 g(x) = f(x) – 1 Moves down 1 Unit p(x) = 4x3 Narrower p(x) = 4f(x) h(x) = (x -1)3 Moves to the right 1 unit h(x) = f(x – 1) k(x) = (x + 2)3 + 1 Moves left 2 units and 1 unit up k(x) = f(x + 2) + 1

  8. Find an equation for each shift of f(x) = x2 g(x) = f(x) + 2 h(x) = f(x+3) p(x) = f(x – 4) + 2 g(x) = x2 + 2 h(x) = (x + 3)2 p(x) = (x – 4)2 + 2

  9. Reflections: h(x) = -f(x) means reflect over the x axis… why? h(x) = f(-x) means reflect over the y axis…why? Original Graph In terms of f(x) In terms of f(x) f(x) = x4 g(x) = -f(x) + 3 h(x) = -f(x – 4) In terms of x In terms of x g(x) = -x4 + 3 h(x) = - (x – 4)4

  10. Order is Important when Graphing!!! RxSRy (reflect over x-axis, shift, reflect over y-axis)

  11. Graph. y = √(2-x) + 3 y = √(-x+2) + 3 Then Graph Rewrite.

  12. Graph. y = -1(x – 3) 3 – 4

  13. Graph. y = -(x+2)3 + 4

  14. Graph. y = (2-x)3 + 4

  15. Consider the following graph. • y = f(x) -1 • y = f(x+1) • y = f(x-1) • y = -f(x-2) • y = f(-x) • y = ½f(x) • y = f(2x)

  16. Exit Pass Describe the sequence of events. The original graph is f(x) = x3 • g(x) = -f(x+3) – 2 • h(x) = f(4-x) • p(x) = f(x-1)-3

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