Writing absolute value equations as piecewise equations

Friday, July 29, Growth Mindset Mistakes Poster A continual focus in my classroom is helping my students build a growth mindset. One quote I've seen time and time again when it comes to mindset is "Mistakes are expected, respected, inspected, and corrected.

Writing absolute value equations as piecewise equations

Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values? What is the difference? Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?

Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? Instructional Implications Model using absolute value to represent differences between two numbers. For example, represent the difference between x and 12 as x — 12 or 12 — x.

Emphasize that each expression simply means the difference between x and Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and Guide the student to write an equation to represent the relationship described in the second problem.

Ask the student to solve the equation and provide feedback. Then explain why the equation the student originally wrote does not model the relationship described in the problem.

Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i. Provide additional opportunities for the student to write and solve absolute value equations. Examples of Student Work at this Level The student: Finds only one of the solutions of the first equation.

Writes the solutions of the first equation using absolute value symbols. Questions Eliciting Thinking How many solutions can an absolute value equation have?

Do you think you found all of the solutions of the first equation? What are the solutions of the first equation? Should you use absolute value symbols to show the solutions?

Instructional Implications Provide feedback to the student concerning any errors made. If needed, clarify the difference between an absolute value equation and the statement of its solutions. Got It The student provides complete and correct responses to all components of the task.

writing absolute value equations as piecewise equations

Examples of Student Work at this Level The student correctly writes and solves the first equation:Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing!

In this lesson, you'll practice different transformations of absolute value graphs. The real absolute value function is continuous everywhere. It is differentiable everywhere except for x = 0. It is monotonically decreasing on the interval (−∞,0] and monotonically increasing on the interval [0,+∞).Since a real number and its opposite have the same absolute value, it is an even function, and is hence not vetconnexx.com real absolute value function is a piecewise linear.

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Mixed Transformations. Most of the problems you’ll get will involve mixed transformations, or multiple transformations, and we do need to worry about the order in which we perform the transformations.. It usually doesn’t matter if we make the x changes or the y changes first, but within the \(x\)’s and \(y\)’s, we need to perform the transformations in the following order.

April 21, Numerical methods John D. Fenton Institute of Hydraulic and Water Resources Engineering, Vienna University of Technology Karlsplatz 13/, Vienna, Austria.

LSC-CyFair Math Department Catalog Description: In-depth study and Applications of Polynomial, rational, radical, absolute-Value, piecewise Defined, Exponential and logarithmic functions, equations, inequalities, graphing skills and systems of equations using matrices.

Absolute value - Wikipedia