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a) We kindly invite to check the image attached below to see a detailed graph of the <em>piecewise</em> function.
b) The <em>piecewise</em> function is continuous.
<h3>How to understand a piecewise function</h3>A <em>piecewise</em> function is a <em>conditional</em> combination of two or more functions, whose expression depends on which value of the domain is the function evaluated at.
a) The <em>piecewise</em> function described in the question is plotted on a graphing tool (i.e. <em>Desmos</em>), whose result is presented in the image attached below.
b) A function is <em>continuous</em> if and only if there is one value from range for every value of domain. The <em>piecewise</em> function is continuous as <em>linear</em> functions are continuous and the two functions of the <em>conditional</em> combination have the same value for x = 30.
To learn more on piecewise functions: brainly.com/question/12561612
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You can convert 1000 to hex and see how many digits that requires:
So every integer below 1000 needs up to 3 digits.
Alternatively, we know that
, and that 
requires 
digits in its hex representation (e.g. 
). Taking the logarithm, we get 
, and adding 1 gives the number of digits needed to represent 
. Similarly,
So every integer below 1000 needs up to 3 digits.
Alternatively, we know that