Absolute Value Equations and Inequalities Review

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What is the definition of absolute value?

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The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

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x = 15 or x = -15.

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It represents the values of x that satisfy -3 \le x \le 3.

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x = 4 or x = -8.

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x = 11 or x = -9.

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The solution is x \ge 6 or x \le -6.

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What is the graphical representation of an absolute value function?

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An absolute value function creates a V-shaped graph that opens upwards.

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What is the relationship between absolute value equations and their corresponding quadratic equations?

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Absolute value equations can often be transformed into quadratic equations by squaring both sides.

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Explain the concept of 'no solution' in absolute value equations.

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An absolute value equation has no solution if the expression inside the absolute value cannot equal the value on the other side.

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What is the significance of the critical points in solving absolute value inequalities?

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Critical points are the values where the expression inside the absolute value equals zero, which helps in determining the intervals to test.