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Proving a composition of monotonic functions is monotonic is easier. You just have to consider the four cases: ($f$ can be increasing-decreasing and so can $g$). I will do the case where $f$ is increasing and $g$ is decreasing and prove $f\circ g$ is monotonic (decreasing).

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Aug 12, 2017 · An estimator (a function that we use to get estimates) that has a lower variance is one whose individual data points are those that are closer to the mean. This estimator is statistically more likely than others to provide accurate answers. The OLS estimator is one that has a minimum variance.

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Improve your math knowledge with free questions in "Checkpoint: Compare functions" and thousands of other math skills.

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In fall of 2008, Sally Keyes (math coach), Kamaljit Sangha (7/8 math teacher/department leader) and Cecilio Dimas (7/8 math teacher) developed our first lesson on cost-analysis. By the end of fall 2008, all eleven 7th grade classes, regular and accelerated, had been taught the DVD Plan lesson. The foundation of this lesson is constructing, communicating, and evaluating student-generated tables ...

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Compare these values to thoes of lake water shown above. Fluid conductivity depends also upon temperature because the mobility of the ions in solution increases with temperature. This behaviour is opposite to that of metallic conductors which involve electronic conduction rather than ionic conduction, and exhibit resistivity increases with ...