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Transformations to Parent Functions

Transformations to Parent Functions. Translation (Shift). A vertical translation is made on a function by adding or subtracting a number to the function. Example: y = x + 3 (translation up) Example: y = x ² - 5 (translation down) A translation up is also called a vertical shift up .

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Transformations to Parent Functions

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  1. Transformations to Parent Functions

  2. Translation (Shift) • A vertical translation is made on a function by adding or subtracting a number to the function. • Example: y = x + 3 (translation up) • Example: y = x² - 5 (translation down) • A translation up is also called a vertical shift up. • A translation down is also called a vertical shift down.

  3. Example: y = |x| + 2 • Parent function (y = |x|) shown on graph in red. The transformation of the parent function is shown in blue. It is a shift up (or vertical translation up) of 2 units.)

  4. Example: y = x - 1 • Parent function (y = x) shown on graph in red. The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit.

  5. Reflection • A reflection on the x-axis is made on a function by multiplying the parent function by a negative. • Multiplying by a negative “flips” the graph of the function over the x-axis. • Example: y = -x² is a reflection of the parent function y = x².

  6. Example: y = - x² The reflection of the parent function is shown in blue. It is a reflection over the x-axis of the function y = x²

  7. Stretch • A stretch is made on a parent function by multiplying the parent function by a number x such that |x| > 1. • Example: y = 3x² • A stretch is also referred to as a narrowing of the graph of the function closer to the y-axis.

  8. Example: y = 2x The blue line shows the graph of the stretch of the parent function, y = 2x, by a scale factor of 2.

  9. Shrink • A shrink is made on a function by multiplying the parent function by a number x such that 0 < |x| < 1. • Example: y = (½) x. • A shrink is also referred to as a widening of the graph of the function closer to the x-axis.

  10. Example: y = (¼) x The blue line shows the graph of the shrink of the parent function, y = (¼)x, by a scale factor of ¼.

  11. What happens when we combine the two (blue is parent function)?

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