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Extra resources for A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers

Sample text

You write the range as k ≥ 3 or, in interval notation, [3, ∞). The outputs can never be less than 3 because the numbers you input are squared. The result of squaring a real number is always positive (or if you input 0, you square 0). If you add a positive number or 0 to 3, you never get anything smaller than 3. ✓ : The range of this function consists of all positive numbers and 0. You write the range as m ≥ 0 or, in interval notation, [0, ∞). The number under the radical can never be negative, and all the square roots come out positive or 0.

You won’t get another number if you input the 3 a second time. The single-output requirement for a function may seem like an easy requirement to meet, but you encounter plenty of strange math equations out there, so watch out. Denoting function notation Functions feature some special notation that makes working with them much easier. The notation doesn’t change any of the properties — it just allows you to identify different functions quickly and indicate various operations and processes more efficiently.

So, if you guessed that the range of the function is every real number except 0, you’re right! You write the range as p ≠ 0, or (–∞, 0) , (0, ∞). Did you also notice that the function doesn’t have a value when x = 5? This happens because 5 isn’t in the domain. Counting on Even and Odd Functions You can classify numbers as even or odd (and you can use this information to your advantage; for example, you know you can divide even numbers by 2 and come out with an integer). You can also classify some functions as even or odd.

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