Mathematics

Problem

: Absolute Value Divided by a Linear Factor a. Define

q:\mathbb{R}\setminus\{2\}\to\mathbb{R}

\displaystyle q(x)=\dfrac{|x^{2}-4|}{x-2}

. Answer the following: b. (i) Express

q(x)

as a piecewise rule without the absolute-value sign, indicating the interval of

x

to which each expression applies. c. (ii) For every interval named in part (i), classify the resulting expression as polynomial, constant, rational or modulus. d. (iii) Simplify each expression wherever possible and state all real numbers (other than

2

) at which

q

is not defined. e. (iv) Determine whether it is possible to define a value

q(2)

so that the extended rule becomes continuous at

x=2

. If it is possible, state that value and justify your answer; if not, give a reason.

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