​Students must write important information and examples in their notes.

​Parent Function of a Linear Function

• Domain: All real numbers

• Range: All real numbers

• x-intercept: 0; y-intercept: 0

​There are 3 types of transformations.

1) Translations

2) Rotation

3) Reflection​

​

​Transformation

- a change in the position or size of a figure.

​f(x - h) where h > 0

The graph will shift h units to the right.

​

f(x + h) where h < 0

The graph will shift h units to the left.​

​​Horizontal Translation

​

​Translation

​

• a type of transformation that moves every point the same distance in the same direction.

​​Vertical Translation

​

​f(x) + k where k > 0

The graph will shift k units up.

​

f(x) - k where k < 0

The graph will shift k units down.​

​a ⋅ f(x) where a > 1

The graph will be steeper (blue graph).​

​​Vertical Stretch

​Rotation

​

– a transformation about a point, like a “turn”.

​​Vertical Shrink

​

​a ⋅ f(x) where 0 < a < 1 (proper fraction or decimal)

The graph will be less steep (red graph).​

​-f(x) where the output is multiplied by a negative value.

​

The graph will be reflected across the x-axis (red graph).​

​​Reflect across the x-axis

​Reflection

​

– a transformation across a line that produces a mirror image, or “flip” over the line.

​Examples

​Students should write the examples in their notes. Example sheet was given in class.

​Answer

​Describe the transformations that occurs in each function.

​Answer

​Describe the transformations that occurs in each function.

​Answer

​Describe the transformations that occurs in each function.

​Answer

​Describe the transformations that occurs in each function.

f(x) is the original function.

​You can look at the graph to describe the function or the equation.

​

Here the graph is less steep therefore it's a vertical shrink by a factor of 1/4. The y-intercept is shifted down 2 units. ​

​

​Answer

​Describe the transformations that occurs in each function.

​Now You Try!

Answer questions #1-4, 8-9 on your example sheet.​

​Students received the example sheet in class. Teacher will discuss the answers at the end of class.