If f(x) = 2x−5, then what is the value of f(2) + f(5) ?

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Presentation transcript:

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?

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

Good Things!!!

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.

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

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!

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

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

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:

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?

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?

Rules for Transformations

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)

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)

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?

Kahoot!!! https://play.kahoot.it/#/k/dc5baf69-9b47-45d8-9030- a0d477ca491d

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?