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Published byEzra Sims Modified over 4 years ago

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Warm-Up: you should be able to answer the following without the use of a calculator 2) Graph the following function and state the domain, range and axis of symmetry for the following function:

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Absolute Value and Exponential Functions and Their Transformations

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Transformations Parabolas Revisited: Vertex Form: y = -a (x – h) 2 + k *Remember that (h, k) is your vertex* Reflection across the x-axis Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider) Horizontal Translation ( opposite of h ) Vertical Translation

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The Parent Graph of the Absolute Value Function

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Vocabulary The function f(x) = |x| is an absolute value function. The highest or lowest point on the graph of an absolute value function is called the vertex. An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images. An absolute value graph has one axis of symmetry that passes through the vertex.

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Absolute Value Function Vertex Axis of Symmetry

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Quadratic and Absolute Value Functions Quadratic and Absolute Value functions share some common characteristics: Vertex Line of Symmetry Minimum/ Maximum point

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Vocabulary The zeros of a function f(x) are the values of x that make the value of f(x) zero. On this graph where x = -3 and x = 3 are where the function would equal 0. f(x) = |x| - 3

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Other Shared Characteristics Review the vertex form of a parabola. Review how the changes in a, h and k transform, reflect or translate the parent graph of a parabola.

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Parent and general equation: Given y=|x| how do you think the general equation of a an absolute value function looks like? How do you think each component transforms, reflects or translates the parent graph?

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Vocabulary A transformation changes a graph’s size, shape, position, or orientation. A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation. When a = -1, the graph y = a|x| is a reflection in the x-axis of the graph of y = |x|.

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Transformations y = -a |x – h| + k *Remember that (h, k) is your vertex* Reflection across the x-axis Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider) Horizontal Translation ( opposite of h ) Vertical Translation

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Example 1:

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Example 2: Graph y = -2 |x + 3| + 4 What is your vertex? What are the intercepts?

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Absolute Value on your calculator

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Graphing example 2 on your calculator

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You Try:

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Example 3: Write a function for the graph shown.

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You Try: Write a function for the graph shown.

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Exponential Functions

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Exponential Parent Graph Key Characteristics: There are no lines of symmetry These functions will always have an asymptote There is no vertex point

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Exponential Parent Graph The ‘locater point’ for this function is the asymptote. Using this as our point allows for quick comparisons between the parent and transformed graphs.

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Exponential Transformation Example #1: 2 Comparing the asymptotes will give the vertical shift.

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Exponential Transformation Example #2: Horizontal translations shift the point where the graph would have crossed the x-axis.

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Exponential General Form Vertical Translation (also the asymptote) Reflection across the x-axis Vertical Stretch a > 1 (makes it narrower) OR Vertical Compression 0 < a < 1 (makes it wider) Horizontal Translation ( opposite of h )

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You Try:

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Homework Worksheet #4

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