Expressions, Equations and Inequalities

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Presentation transcript:

Expressions, Equations and Inequalities Ch. 2.7 Absolute Value Functions and Graphs EQ: How can we graph absolute value functions? I will graph absolute value functions.

Bell Work Write an equation for each transformation of y = x^2. Vertical stretch by a factor of 4. Vertical compression by a factor of ¼. Move to the left 5 units, and to up 3 units. Move to the right 3 units, and down 2 units. EQ: How can we graph absolute value functions? I will graph absolute value functions.

2.6 continued- Compression/Stretch EQ: How can we graph absolute value functions? I will graph absolute value functions.

Absolute Value Functions and Graphs READ We can apply translations, stretches, compressions, and reflections to any parent function f(x). The absolute value function is a particularly good parent function to use for these transformations since it has an easily recognizable V shape. This lesson discusses vertical stretches and compressions (those in which all y-coordinates are multiplied by a common factor). Make tables of ordered pairs can help you analyze the effects of the transformations on each coordinate. EQ: How can we graph absolute value functions? I will graph absolute value functions.

The Absolute Value parent function, f(x)=|x| EQ: How can we graph absolute value functions? I will graph absolute value functions.

Graphing an Absolute Value Function EQ: How can we graph absolute value functions? I will graph absolute value functions.

Graphing an Absolute Value Function Now you try… What is the graph of the function y = |x| + 2? How is this different from the parent function? EQ: How can we graph absolute value functions? I will graph absolute value functions.

Concept Summary EQ: How can we graph absolute value functions? I will graph absolute value functions.

Stop and talk… Discussion points… How is the concept about parent functions related to graph absolute value functions? How is it different? What technique(s) can be use to graph absolute value functions? EQ: How can we graph absolute value functions? I will graph absolute value functions.

Practice Absolute value transformations F(X) = |X| Green F(x) = |X| + 2 Black F(X) = |X| -5 Light blue F(X) = -|x| Red F(X) = ½ |X| Orange F(X) = 3|X| Brown F(X) = |X-4| Yellow F(X) = |X + 3| Pink EQ: How can we graph absolute value functions? I will graph absolute value functions.

Concept Summary Problem 5 EQ: How can we graph absolute value functions? I will graph absolute value functions.

Identifying Transformations Without graphing, what are the vertex and axis of symmetry of the graph of y=3|x-2|+4? How is the parent function transformed? EQ: How can we graph absolute value functions? I will graph absolute value functions.

Identifying Transformations What are the vertex and axis of symmetry of Y= -2|x-1| -3? EQ: How can we graph absolute value functions? I will graph absolute value functions.

Poster Project Due Monday, 9/14 EQ: How can we graph absolute value functions? I will graph absolute value functions.

Closure (On your bell sheet) Explain… How can we graph absolute value functions? Why are absolute value functions perfect for applying transformations? How is graphing absolute value functions similar to graphing parabolas? How is it different? EQ: How can we graph absolute value functions? I will graph absolute value functions.