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the range is all real numbers

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Q: Which is not a characteristic of the absolute value parent function?

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It’s vertex is not at the origin

The absolute value function returns the absolute value of a number.

Its vertex is not at the origin

An absolute-value function

No it is not

No, There exists a counter example in the page 244 of the book Grimmett & Stirzaker, One thousand exercises in probability. The example is a Bernoulli random variable with parameter 1/3.

f(x) = |f(x)|/3

The absolute value of a function changes the original function by ensuring that any negative y values will in essence be positive. For instance, the function y = absolute value (x) will yield the value +1 when x equals -1. Graphically, this function will look like a "V".

Absolute Value function

I

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