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ACC Module#2 Unit 2.6

ACC Module#2 Unit 2.6

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ACC Module#2 Unit 2.6

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  1. DemingEarly College High SchoolUnit 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6 Linear Applications and Graphs

  2. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6 Linear Applications and Graphs 2.6.1 Graphing Functions and Relations To graph relations and functions, the Cartesian plane is used. This means to think of the plane as being a grid of squares, with one direction being the x-axis and the other direction being the y-axis.

  3. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations For functions, generally, the independent variable is placed along the x-axis, and the dependent variable is placed along the vertical axis. Any point on the plane can be specified by saying how far to go along the x-axis and how far along the y-axis with a pair of numbers(x,y).Negative values mean to move left or down from the origin; positive values mean to move right or up. The point where the axes cross one another is called the origin. The origin has coordinates (0, 0) and is usually called “0” when given a specific label.

  4. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations

  5. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Fill in the table and graph the function: f(x) = 5x +1

  6. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Fill in the table and graph the function: f(x) = 5x +1

  7. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Fill in the table and graph the function: f(x) = 3x - 6

  8. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Fill in the table and graph the function: f(x) = 3x - 6

  9. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Relations also can be graphed by marking each point whose coordinates satisfy the relation. If the relation is a function, then there is only one value of y for any given value of x. This leads to the vertical line test: if a relation is graphed, then the relation is a function if any possible vertical line drawn anywhere along the graph would only touch the graph of the relation in no more than one place.

  10. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Express the following relations as a set of ordered pairs.

  11. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Express the following relations as a set of ordered pairs.

  12. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations When we plot these ordered pairs, we find out they are relations, not functions and we just get a number of point pairs.

  13. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Plot these ordered pairs.

  14. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.1 Graphing Functions and Relations Plot these ordered pairs. Again they are not a function.

  15. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.2 Rate of Change The rate of change for a linear function is constant and can be determined based on a few representations. One method is to place the equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this graph (y = x +1), the slope is 1 and the y-intercept is 1. For every horizontal change of +1 unit, there is a vertical change of +1 unit. In this case, the x-intercept is -1, which is the point where the line crosses the x-axis.

  16. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.2 Rate of Change Rate of change = slope = m = Find the slope from a graph. Pick any two points,

  17. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.6.2 Rate of Change Rate of change = slope = m = Find the slope from a graph. Pick any two points,

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