Absolute value functions have a V-shape and model situations involving distance or edges. The graph can be transformed by changing the slope (a), shifting the vertex horizontally (h), or shifting the vertex vertically (k). To graph, identify the vertex and axis of symmetry, then use the slope to sketch the right side and symmetry to complete the left. Writing the equation involves identifying the vertex (h, k) and slope (a).
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
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This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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2. Absolute Value Functions
• The absolute value of x is defined by:
• The graph of y = |x| looks like a v-shape.
vertex
3. Why are they important?
• Have you ever played pool or putt-putt
golf?
• The path of the ball when making a bank
shot is an example of an absolute value
function.
4. Transformations
• There are four ways the absolute value graph
can be changed:
1. Open Up or Open Down
2. Change in Width – sides can be steeper or
less steep
3. Horizontal Shift – vertex moves left or right
4. Vertical Shift- vertex moves up or down
5. General Form
• y = a |x – h| + k
• Effects of a:
• When a > 0 (positive), the V opens up.
• When a < 0 (negative), the V opens down.
• When |a| < 1, the sides are less steep than
y = |x|.
• When |a| > 1, the sides are steeper than
y = |x|.
11. Graphing Absolute Value Functions
• Plot the vertex.
• Sketch the axis of symmetry.
• Use a (the slope) to graph the right side.
• Use symmetry to draw in the left side.
• Example:
Graph
