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GeoGebraGeoGebra Classroom

Explore Function Translations

Essential Questions:

1. What similarities exists between function translations? 2. How does f(x) change based on a, h, and k?

Linear Function Translations

Linear Function (Point Slope Form) Use the green, red, and blue buttons to observe the effect of a, h, and k Answer the following questions 1. How does a affect the graph? 2. How does h affect the graph? 3. How does k affect the graph?

Linear Function Translations

Quadratic Function Translations

Quadratic Function (Vertex Form) Use the green, red, and blue buttons to observe the effect of a, h, and k Answer the following questions 1. How does a affect the graph? 2. How does h affect the graph? 3. How does k affect the graph?

Quadratic Function Translations

Radical Function Translations

Radical Function Use the green, red, and blue buttons to observe the effect of a, h, and k Answer the following questions 1. How does a affect the graph? 2. How does h affect the graph? 3. How does k affect the graph?

Radical Function Translations

Hyperbolic Function Translations

Hyperbolic Function Use the green, red, and blue buttons to observe the effect of a, h, and k Answer the following questions 1. How does a affect the graph? 2. How does h affect the graph? 3. How does k affect the graph?

Hyperbolic Function Translations

Conclusions

Given any function f(x), how might you expect f(x-3) to behave?

Given any function f(x), how might you expect f(x)+5 to behave?

Given any function f(x), how might you expect -3f(x) to behave?