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Quadratics, The Root Function & Inverses

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2.7: Absolute Value Functions and Graphs

2.7: Absolute Value Functions and Graphs. Objective: SWBAT graph an absolute value function by performing transformations on the parent function f ( x ) = | x |. Vocabulary. The function f(x) = |x| is an absolute value function .

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Chapter 2 Functions and Graphs

Chapter 2 Functions and Graphs. Section 2 Elementary Functions: Graphs and Transformations. Identity Function. Domain: R Range: R. Square Function. Domain: R Range: [0, ?). Cube Function. Domain: R Range: R. Square Root Function. Domain: [0, ?) Range: [0, ?).

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Finding the equation of a sine or cosine curve from the graph

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Absolute Value Graphs

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Combining several transformations The order is very important

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1.7 Motion in the Coordinate Plane

1.7 Motion in the Coordinate Plane. Objectives: -Review algebraic concepts including the coordinate plane, origin, x- and y- coordinates, and ordered pair. -Construct translations, reflections across axes, and rotations about the origin of the coordinate plane. Warm-Up:

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6.4 Absolute-Value Functions

6.4 Absolute-Value Functions. Objectives: Explore features of the absolute-value function. Explore basic transformations of the absolute-value function .

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Completing the Square

Completing the Square. Section 5.4. -. -. -. -. Ex. -. Solve by completing the square. Solve by completing the square. Day 2 Vertex form. The coordinates of the vertex of the graph

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2.4 Use Absolute Value Functions and Transformations

2.4 Use Absolute Value Functions and Transformations. 2.4-2.5 Quiz: Friday. Vocabulary. The function f(x) = |x| is an absolute value function . The highest of lowest point on the graph of an absolute value function is called the vertex .

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Warm Up

Warm Up. Reflect the following image across the line. Motion in the Coordinate Plane. Transformations. Graphing Ordered Pairs. Now Plot P(5, 6). Horizontal/Vertical Translations.

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Exponential Functions

Exponential Functions. Definition of Exponential Functions. The exponential function f with a base b is defined by f(x) = b x where b is a positive constant other than 1 (b > 0, and b ? 1) and x is any real number. So, f(x) = 2 x , looks like:. Graphing Exponential Functions.

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Finding the equation of a sine curve from the graph

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Pre-Cal

Pre-Cal. Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations. Definitions. Transformations : operations that change the location, orientation, or size of a graph.

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6-8: Graphing Absolute Value Equations

6-8: Graphing Absolute Value Equations. Objective: To graph absolute value equations by using translation. Absolute Value Equations . ACTIVITY Graph: y = IxI Now, graph: y = IxI + 2 Describe how the graphs are the same and how they are different. Translation.

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Transformations of quadratic and linear functions

Transformations of quadratic and linear functions. Guiding Questions: What rules from transformations can we use to translate linear and quadratic functions? How can we use quadratic transformations to analyze changes in distance?. Linear and quadratic parent functions.

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Graphing Quadratic Functions using Transformational Form

The Transformational Form of the Quadratic Equations is:. Graphing Quadratic Functions using Transformational Form. Graphing Quadratic Functions using Transformational Form. The Transformational Form of this Quadratic Equations is:. This also provides the following information:

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5.9 Transforming Polynomial Functions

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Cosine and Sine Graphs

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