Directions: For the following piecewise functions, find the value of $k$ that makes the function continuous, or state that no such value exists.
26. $f(x)=\left\{\begin{array}{cc}\frac{9 x^2-4}{3 x+2}, & \text { if } x \neq-\frac{2}{3} \\ k, & \text { if } x=\frac{2}{3}\end{array}\right.$
27. $g(x)=\left\{\begin{array}{ll}x^2-2, & \text { if } x<3 \\ k x+4, & \text { if } x \geq 3\end{array}\right.$
28. $h(x)=\left\{\begin{array}{ll}3 x-1, & \text { if } x<2 \\ \ln (k), & \text { if } x \geq 2\end{array}\right.$
29. $p(x)=\left\{\begin{array}{cc}\frac{x^2-x-6}{x^2-4}, & \text { if } x \leq-2 \\ k x^2, & \text { if } x>-2\end{array}\right.$
Answer (3)
144 196 256 324 400 484
121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. ;
The perfect squares between 100 and 500 that are even numbers are 144, 196, 256, 324, 400, and 484. These numbers are all the squares of integers from 10 to 22 that result in an even number. They illustrate the relationship between even numbers and perfect squares within the specified range.
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