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 = x² - 5 (translation down) A translation up is also called a vertical shift up. A translation down is also called a vertical shift down.

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.)

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.

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.

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

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.

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

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.

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.

Guided Practice: Identify the transformations performed on the parent function. (Hint: First, identify the parent function.) 1. y = -4x + 7 2. y =

Describe the transformation done on the function.

Describe the transformation done on the function.

Describe the transformation done on the function.

Describe the transformation done on the function.

Describe the transformation done on the function.

Sketch the following transformations. Hint: When sketching it is not necessary for the graph to be exact but it should be close. 1. 2. 3.