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Understanding Vertical Shifts in Functions: A Review of Graph Translations

In this review, we explore vertical shifts in various parent functions including linear, quadratic, cubic, absolute value, square root, and inverse functions. Each function type is illustrated with specific equations showing how vertical shifts affect their graphs. For instance, we examine linear functions like y = x + 2 and y = x - 3, as well as quadratic functions such as y = x² + 1 and y = x² - 4. Utilize our graph calculator links for visual understanding and better grasping how these transformations impact function behavior.

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Understanding Vertical Shifts in Functions: A Review of Graph Translations

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  1. Transforming Functions Part 1: Vertical Shifts

  2. Review of Parent Graphs • Linear • y = x • Quadratic • y = x2 • Cubic • y = x3 • Absolute Value • Y = IxI • Square Root • Y = √x • Inverse • Y = 1/x

  3. Vertical Shift: Linear Functions • y = x + 2 • y = x – 3 http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  4. Vertical Shift: Quadratic Functions • y = x2 + 1 • y = x2 – 4http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  5. Vertical Shift: Cubic Functions • y = x3 + 5 • y = x3 – 2http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  6. Vertical Shift: Absolute Value Functions • y = IxI + 3 • y = IxI – 5http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  7. Vertical Shift: Square Root • y = √x + 2 • y = √x – 3http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

  8. Vertical Shift: Linear Functions • y = 1/x + 3 • y = 1/x – 2 http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

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