Warm Up – August 23, 2017 How is each function related to y = x?

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Presentation transcript:

Warm Up – August 23, 2017 How is each function related to y = x? y = x – 3 2. y = 2x 3. y = -4x Write an equation for each vertical translation of y = x. 4. 2/3 unit down 5. 4 units up Write the function rule for the function related in the given axis. 6. f(x) = 3x; y-axis Write the function rule g(x) after the given transformation of the graph f(x) = 4x. 7. Translated up 5 units; reflection in the y-axis 8. Reflection in the y-axis; vertical compression by a factor of 1/8.

2.7 Absolute‐Value Functions and Graphs Learning Target: I can graph absolute‐value functions. Key Terms: absolute‐value functions, axis of symmetry, vertex

Absolute‐value functions – function of the form f(x) = |mx + b| + c, where m ≠ 0, is an absolute value function. Axis of symmetry – the line that divides a figure into two parts that are mirror images. Vertex – single maximum or minimum of a graph

Absolute-Value Parent Function f(x) = |x|

“I do” Graphing an Absolute‐Value Function What is the graph of the absolute value function y = |x| ‐ 4? How is this graph different from the graph of the parent function y = |x|?

“You do” What is the graph of the function y = |x| + 2? How is this graph different from the parent function? Do transformations of the form y = |x| + k affect the axis of symmetry? Explain.

The Family of Absolute Value Functions Parent Function y = |x| Vertical Translation Horizontal Translation Translation up k units, k > 0 y = |x| + k Translation down k units, k > 0 y = |x| - k Translation up h units, h > 0 y = |x – h| Translation down h units, h > 0 y = |x + h| Vertical Stretch and Compression Vertical stretch, a > 1 y = a|x| Vertical compression, 0 < a < 1 Reflection In the x-axis y = -|x| In the y-axis y = |-x|

“I do” Combining Translations What is the graph of y = |x + 2| + 3?

“You do” What is the graph of y = |x – 2| + 1?

“I do” Vertical Stretch and Compression What is the graph of y = ½|x|?

“You do” What is the graph of y = 2|x|?

General Form of the Absolute Value Function y = a|x – h| + k The stretch or compression factor is |a|, the vertex is located at (h, k), and the axis of symmetry is the line x – h

“I do” 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 y = |x| transformed?

“You do” What are the vertex and axis of symmetry of y = ‐2|x – 1| ‐ 3? How is y = |x| transformed?

Homework Pg. 111 # 10, 12, 16, 17, 18, 23, 24, 32