Exploring Transformations and Parent

Graphs1-8 and 1-9

Learning Targets • Students will be able to apply and describe

transformations• Students will be able to identify parent graphs

Standards • Building new functions from existing functions

o identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

o CCSS.MATH.CONTENT.HSF.BF.B.3

Image Notice• All images used are either made by me or

accessed on google using the labeled for reuse search filter.

Parent Graphs

Constant Linear

Quadratic

Constant

CubicSquare root

Images created by me using Kuta Software

Transformations: Translation

• Transformation: Change in the position, size, or shape of a figure

• Translation: slide each point the same distance in the same direction.

• Horizontal translations: each point shifts right or left by a number of units

• Vertical translation: each point shifts up or down by a number of units

• Note: can have both horizontal and vertical translation—for example: three units up and two left

Transformation: Reflection

• Reflection across the y-axiso X coordinate changes, y coordinate stays the same

• Reflection across the x-axiso Y coordinate changes, x coordinate stays the same

Transformation: Stretches and Compression

• Horizontal stretch: each point is pulled away from the y-axiso X coordinate changes

• Horizontal compression: each point is pushed toward the y-axiso X coordinate changes

• Vertical stretch: each point is pulled away from the x-axiso Y coordinate changes

• Vertical compression: each point is pushed toward the x-axiso Y coordinate changes