Mathematics

Problem

For

h(x)=\dfrac{x^{2}-4}{x^{2}-x-2}

, answer the following: (i) Write

h(x)

in its simplified form. (ii) Determine the domain of

h

. (iii) Determine the range of

h

, specifying any missing

y

-value.

Intuitive explanation

Rational functions reveal their true behavior once you factor and cancel—but cancellation creates a hole, not just a simplified expression. Start by factoring both numerator and denominator completely, then cancel common factors to see the simplified form. This tells you which points are excluded from the domain and helps you find any $y$ -values the function can never reach, even though the simplified form might suggest otherwise.

Intuitive explanation

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