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Mastering Graph Shifts and Sketches in Algebra

In this engaging final class, students will practice quick sketches of six key functions and learn how to shift graphs vertically and horizontally. By the end, they will know how to identify and apply vertical shifts (up and down) and horizontal shifts (left and right). The lesson emphasizes how positive and negative constants affect graph positions, and students will also explore graph reflections. This interactive session includes a fun team competition with prizes to reinforce learning.

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Mastering Graph Shifts and Sketches in Algebra

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  1. Practice with Quick Sketches

  2. Last Class… • Vertical Line Test • Quick Sketches of 6 Important Functions

  3. Learning Targets By the end of class, students will be able to: • Quick sketch 6 common functions • Use shifting to move graphs

  4. Shifting • Two Types of Shifts • Vertical shifts: Up and down • Horizontal Shifts: Left and Right

  5. Vertical Shifts • A VERTICAL SHIFT is given by a +/- constant next to the variable term • Examples: • f(x) = x + 3 Compared to our quick sketch of f(x) = x, the graph is shifted 3 units UP

  6. Vertical Shifts • Whether the shift is UP or DOWN depends on the sign in front of the number • Positive: Graph shifts UP • Negative: Graph shifts DOWN

  7. Horizontal Shifts • A HORIZONTAL SHIFT is given by a +/- constant inside the parenthesis or radical sign • Example: f(x) = (x – 3)2 Compared to the quick sketch of the function f(x) = x2, the sketch of our function is moved 3 units to the right.

  8. Horizontal Shifts • Whether the shift is LEFT or RIGHT depends on the sign in front of the number • Positive: Graph shifts LEFT • Negative: Graph shifts RIGHT

  9. “Flipping” • When there is a NEGATIVE sign in front of your function, that means that you turn the function upside down, or 90° • Example: f(x) = -|x| Compared to the quick sketch of the function f(x) = |x|, the sketch of our function is turned upside down.

  10. One person from each group needs to grab… A white board A marker An eraser

  11. “Lightning” Round • You will have 1 minute to sketch the given graph • Point goes to the every group who gets it right • Group with the most points at the end of the period gets a prize (candy)

  12. f(x) = x2

  13. f(x) = (x – 1)3

  14. f(x) = -|x| - 2

  15. f(x) = x + 5

  16. f(x) = √x

  17. f(x) = -x2 + 3

  18. f(x) = √(x – 1) + 3

  19. f(x) = (x + 3)2 – 2

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