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IBMathsDPAnalysis & Approaches (AA)HLFlashcards2. FunctionsInequalities

Inequalities (DP IB Analysis & Approaches (AA))

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  • How can you rewrite the inequality f open parentheses x close parentheses less or equal than g open parentheses x close parentheses to solve it graphically?

    You can rewrite the inequality f open parentheses x close parentheses less or equal than g open parentheses x close parentheses as f open parentheses x close parentheses minus g open parentheses x close parentheses less or equal than 0, solve to find the zeros, and graph it to find the intervals of x that satisfy the inequality.

  • What do the zeros of f open parentheses x close parentheses minus g open parentheses x close parentheses represent graphically?

    The zeros of f open parentheses x close parentheses minus g open parentheses x close parentheses represent the x-coordinates of the points of intersection of the graphs y equals f open parentheses x close parentheses and y equals g open parentheses x close parentheses.

  • True or False?

    When rearranging inequalities, you should always flip the sign when multiplying or dividing.

    False.

    When rearranging inequalities, you should not always flip the sign when multiplying or dividing.

    You only flip the sign when multiplying or dividing by a negative value.

  • Why should you never multiply or divide both sides of an inequality by a variable?

    You should never multiply or divide both sides of an inequality by a variable as the variable could be either positive or negative and could potentially change the direction of the inequality.

  • True or False?

    Taking reciprocals of positive values always preserves the direction of an inequality.

    False.

    Taking reciprocals of positive values does not preserve the direction of an inequality, it reverses the direction of the inequality.

  • When does taking logarithms reverse the direction of an inequality?

    Taking logarithms reverses the direction of an inequality when the base is between 0 and 1 open parentheses 0 less than a less than 1 close parentheses.

  • What is the first step in solving a polynomial inequality?

    The first step in solving a polynomial inequality is to rearrange the inequality so that one side is equal to zero, e.g. P open parentheses x close parentheses less or equal than 0.

  • Which two main methods can you use to solve a polynomial inequality if you know its roots?

    The two main methods can you use to solve a polynomial inequality if you know its roots are:

    • graphing the inequality,

    • or using the sign table method.

  • When should you use the sign table method to solve a polynomial inequality?

    The sign table method can be used to solve a polynomial inequality when you are unsure how to sketch the graph of the polynomial.

  • What are the steps involved in the sign table method for solving a polynomial inequality?

    The sign table method for solving a polynomial inequality includes the following steps:

    • Split the real numbers into possible intervals using the roots of the polynomial.

    • Test a value from each interval to see if it satisfies the inequality.

    • Choose the intervals that satisfy the inequality as parts of the solution.

  • Can the solution to a polynomial inequality be a single point?

    Yes, in some cases the solution to a polynomial inequality can be a single point.

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