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Holt Algebra 1 5-Ext Absolute-Value Functions 5-Ext Absolute-Value Functions Holt Algebra 1 Lesson Presentation Lesson Presentation

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Holt Algebra 1 5-Ext Absolute-Value Functions Graph absolute-value functions. Identify characteristics of absolute- value functions and their graphs. Objectives

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Holt Algebra 1 5-Ext Absolute-Value Functions absolute-value function axis of symmetry vertex Vocabulary

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Holt Algebra 1 5-Ext Absolute-Value Functions An absolute-value function is a function whose rule contains an absolute-value expression. To graph an absolute-value function, choose several values of x and generate some ordered pairs.

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Holt Algebra 1 5-Ext Absolute-Value Functions Absolute-value graphs are V-shaped. The axis of symmetry is the line that divides the graph into two congruent halves. The vertex is the corner" point on the graph.

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Holt Algebra 1 5-Ext Absolute-Value Functions From the graph of y = |x|, you can tell that: the axis of symmetry is the y-axis (x = 0). the vertex is (0, 0). the domain (x-values) is the set of all real numbers. the range (y-values) is described by y 0. y = |x| is a function because each domain value has exactly one range value. the x-intercept and the y-intercept are both 0.

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Holt Algebra 1 5-Ext Absolute-Value Functions Graph the absolute-value function and label the axis of symmetry and the vertex. Identify the intercepts, and give the domain and range. Example 1A: Absolute-Value Functions y = |x| + 1 Choose positive, negative, and zero values for x, and find ordered pairs. Plot the ordered pairs and connect them. y = |x| + 1 x –2 – Axis of symmetry Vertex

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Holt Algebra 1 5-Ext Absolute-Value Functions Example 1A Continued the axis of symmetry is the y-axis (x = 0). the vertex is (0, 1). there are no x-intercepts. the y-intercept is +1. the domain is all real numbers. the range is described by y 1. From the graph you can tell that Axis of symmetry Vertex

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Holt Algebra 1 5-Ext Absolute-Value Functions Graph the absolute-value function and label the axis of symmetry and the vertex. Identify the intercepts, and give the domain and range. Example 1B: Absolute-Value Functions y = |x – 4| Choose positive, negative, and zero values for x, and find ordered pairs. Plot the ordered pairs and connect them. y = |x – 4| x – Axis of symmetry Vertex

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Holt Algebra 1 5-Ext Absolute-Value Functions the axis of symmetry is x = 4. the vertex is (4, 0). the x-intercept is +4. the y-intercept is +4. the domain is all real numbers. the range is described by y 0. From the graph you can tell that Example 1B Continued Axis of symmetry Vertex

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Holt Algebra 1 5-Ext Absolute-Value Functions Graph the absolute-value function and label the axis of symmetry and the vertex. Identify the intercepts, and give the domain and range. f(x) = 3|x| Choose positive, negative, and zero values for x, and find ordered pairs. Plot the ordered pairs and connect them. f(x) = 3|x| x –2 – Check It Out! Example 1 Axis of symmetry Vertex x

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Holt Algebra 1 5-Ext Absolute-Value Functions Check It Out! Example 1 Continued the axis of symmetry is x = 0. the vertex is (0, 0). the x-intercept is 0. the y-intercept is 0. the domain is all real numbers. the range is described by y 0. From the graph you can tell that Axis of symmetry Vertex x

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