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The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions.
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- 6 Years Ago Posted 6 Years Ago. Direct Link to David Severin's Post “No, If It is Positive It
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- Graphing Absolute Value Functions
Y is equal is to the absolute value of x plus three. Now in...
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Given an absolute value function, solve for the set of inputs where the output is positive (or negative). Set the function equal to zero, and solve for the boundary points of the solution set. Use test points or a graph to determine where the function’s output is positive or negative.
To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero.
Definition and properties. Real numbers. For any real number , the absolute value or modulus of is denoted by , with a vertical bar on each side of the quantity, and is defined as [8] The absolute value of is thus always either a positive number or zero, but never negative.
This topic covers: - Solving absolute value equations - Graphing absolute value functions - Solving absolute value inequalities.
Knowing how to solve problems involving absolute value functions is useful. For example, we may need to identify numbers or points on a line that are at a specified distance from a given reference point. An absolute value equation is an equation in which the unknown variable appears in absolute value bars. For example,
Properties of Absolute Value. Let \ (a\), \ (b\) and \ (x\) be real numbers and let \ (n\) be an integer. a Then. Product Rule: \ (|ab|= |a||b|\) Power Rule: \ (\left| a^ {n} \right| = |a|^ {n}\) whenever \ (a^ {n}\) is defined. Quotient Rule: \ (\left| \dfrac {a} {b} \right| = \dfrac {|a|} {|b|}\), provided \ (b \neq 0\) Equality Properties:
