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Graphing Transformations of Mathematical Functions

Learn how to graph various functions by applying transformations such as shifts, flips, and stretches. Examples include quadratic, cubic, hyperbola, square root, exponential, linear, absolute value, and circle functions.

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Graphing Transformations of Mathematical Functions

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  1. Graphing Form

  2. Graphing Form ( h, k ):The Key Point The value of a

  3. Example: Quadratic Transformation: Shift the parent graph three units to the right and four units up. New Equation: y = 4 (3,4) x = 3

  4. Example: Cubic Transformation: Flip the parent graph and shift it five units up. Transformation: y = 5 New Equation: (0,5) x = 0

  5. Example: Hyperbola Transformation: Shift the parent graph four units to the left and three units down. Transformation: New Equation: (-4,-3) y = -3 x = -4

  6. Example: Square Root Transformation: Shift the parent graph six units to the left. Transformation: x = -6 New Equation: y = 0 (-6,0)

  7. Example: Exponential Transformation: Transformation: Shift the parent graph five units to the right and two units up. Then stretch the graph by a factor of 3. New Equation: a = 3 (5,2) y = 2 x = 5

  8. Linear Function Parent Equation Graphing Form (h,k) Point: Slope: Unless specified, you do not need to have the answer in y=mx+b form!

  9. Example: Linear Transformation: A line with slope ½ that passes through the point (-6,4). Slope = ½ New Equation: y = 4 (-6,4) x = -6 Point Slope

  10. Absolute Value Function Parent Equation Graphing Form • MATH • Right to NUM • 1. abs( Absolute value can be found in the calculator:

  11. Example: Absolute Value Transformation: Flip the parent graph and shift it three units to the left and four units up. Transformation: (-3,4) New Equation: y = 4 x = -3

  12. Equation for a Circle Example (0,0) Center: Radius: Graphing Form (h,k) Center: Radius:

  13. Example: Circle Transformation: A circle centered at (4,-1) whose radius is 4. Transformation: x = 4 New Equation: (4,-1) y = -1 (4,-1) Center: Radius: Is a circle a function? NO!

  14. Logarithmic Function Parent Equation Graphing Form

  15. Example: Exponential Transformation: Shift the parent graph three units to the right and two units up. Transformation: New Equation: y = 2 x = 3

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