2. If f(x) = 2x−5, then what is the value of f(2) + f(5) ?
Do Now 5/30
If f(x) = 2x−5, then what is the value of f(2) + f(5) ?
Essential Question: How do I perform transformations?

3. Agenda
Do Now
Good Things
Unit 1 Review Guided Notes – Transformations

4. Good Things!!!

5. Functions – Inputs and Outputs
A function is a mathematical relation so that every input in the domain corresponds with one output in the range. To evaluate a function, f(x), substitute the domain values for every x and calculate.

6. Function Notation Example
Evaluate f(-3) for f(x) = 100(2)x
If f(x,y) = (3x, 5y), then what is f(1, -2)?
Substitute: 100(2)-3
Solve: 100 * 0.125
12.5

7. Guided Notes – Function Notation
Input = domain of the function = x-values
Output = range of the function = y values X y
range
domain
input
output
Alphabetical order!

8. Guided Notes: Function Notation
Vertical Line Test: If a vertical line crosses the graph once, the graph is a function

9. Guided Notes - Transformations
Transformations are function rules that are applied to coordinates to create a new shape.
PREIMAGE  IMAGE

10. Transformations
Rigid transformations preserve the shape and produce congruent figures
Translations
Reflections
Rotations
Any combination of these!
To prove if a transformation preserves rigid motion, you can use the distance formula:

11. Dilations Length of image side = Scale Factor Length of pre-image side
To determine the coordinates for a dilation, multiply each point times the scale factor of the dilation.
Length of image side
Length of pre-image side
= Scale Factor
The coordinates of triangle CDE are as follows:
C (3, 6)
D (9, 6)
E (6, 12)
The triangle is dilated by a scale factor of 2/3.
1. What are the new coordinates of triangle C’D’E’?
2. Is this an enlargement, congruency, or a reduction?

12. Dilations Practice
The image of a point after a dilation of scale factor 3 is (6,15). What was the original location of the point?

13. Rules for Transformations

14. Rules for Transformations
Reflection Over the x-axis
Function Rule: (x,y)  (x, -y)
Reflection Over the y-axis
Function Rule: (x,y)  (-x, y)
Reflection Over the y=x line
Function Rule: (x,y)  (y, x)
Reflection Over the y= -x line
Function Rule: (x,y)  (-y, -x)

15. Rules for Transformations
Translation
Function Rule: (x,y)  (x + h, y + a)
Rotation of 90o
Function Rule: (x,y)  (-y, x)
Rotation of 180o
Function Rule: (x,y)  (-x, -y)
Rotation of 270o
Function Rule: (x,y)  (y, -x)

16. Transformations Practice
What are the coordinates of the point (1,-2) after a reflection over the x-axis?
What are the coordinates of the point (-7, 4) after it is rotated 90o?
What are the coordinates of the point (2, -3) after it is reflected over the x-axis and then rotated 90o?

17. Kahoot!!!
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18. Exit Ticket
1. The point J(8, -6) undergoes the translation of T-4, -2. What are the coordinates of J’?
2. What transformation is shown in the diagram?