Let $f(x)=\{\begin{array}{ll}{x}^2-k& x\le 3\\ -2x+2k& x>3\end{array}$. Which equation must hold for $f$ to be continuous at $x=3$?

Let $h(x)=\{\begin{array}{ll}\frac{1}{x+4}& x<-4\\ k& x\ge -4\end{array}$. For what value of $k$ is $h$ continuous at $x=-4$?

Let $u(x)=\{\begin{array}{ll}-3x+k& x<-4\\ x^2+1& x\ge -4\end{array}$. For what value of $k$ is $u$ continuous at $x=-4$?

Let $g(x)=\{\begin{array}{ll}\frac{x^2-9}{x-3}& x\ne 3\\ c& x=3\end{array}$. For what value of $c$ is $g$ continuous at $x=3$?

Let $f(x)=\{\begin{array}{ll}6x+k& x<3\\ x^2+3& x\ge 3\end{array}$. For what value of $k$ is $f$ continuous at $x=3$?

Let $u(x)=\{\begin{array}{ll}6x+k& x<-3\\ x^2-6& x\ge -3\end{array}$. For what value of $k$ is $u$ continuous at $x=-3$?

Let $g(x)=\{\begin{array}{ll}\frac{x^2-81}{x+9}& x\ne -9\\ c& x=-9\end{array}$. For what value of $c$ is $g$ continuous at $x=-9$?

Let $g(x)=\{\begin{array}{ll}\frac{x^2-16}{x+4}& x\ne -4\\ c& x=-4\end{array}$. For what value of $c$ is $g$ continuous at $x=-4$?

Let $g(x)=\{\begin{array}{ll}-6x+k& x<-4\\ x^2+9& x\ge -4\end{array}$. For what value of $k$ is $g$ continuous at $x=-4$?

Let $p(x)=\{\begin{array}{ll}-3x+k& x<-1\\ x^2-8& x\ge -1\end{array}$. For what value of $k$ is $p$ continuous at $x=-1$?

Let $u(x)=\{\begin{array}{ll}-x+k& x<4\\ x^2-4& x\ge 4\end{array}$. For what value of $k$ is $u$ continuous at $x=4$?

Let $f(x)=\{\begin{array}{ll}ax+b& x<1\\ 6& x=1\\ 4ax-5b& x>1\end{array}$. Which pair $\left(a,b\right)$ makes $f$ continuous at $x=1$?

Let $f(x)=\{\begin{array}{ll}ax+b& x<1\\ 9& x=1\\ 4ax-5b& x>1\end{array}$. Which pair $\left(a,b\right)$ makes $f$ continuous at $x=1$?

Let $f(x)=\{\begin{array}{ll}ax+b& x<1\\ 9& x=1\\ 2ax-b& x>1\end{array}$. Which pair $\left(a,b\right)$ makes $f$ continuous at $x=1$?

Let $h(x)=\{\begin{array}{ll}\frac{1}{x-7}& x<7\\ k& x\ge 7\end{array}$. For what value of $k$ is $h$ continuous at $x=7$?

Let $g(x)=\{\begin{array}{ll}-x+k& x<1\\ x^2+9& x\ge 1\end{array}$. For what value of $k$ is $g$ continuous at $x=1$?

Let $f(x)=\{\begin{array}{ll}ax+b& x<1\\ 8& x=1\\ 2ax-2b& x>1\end{array}$. Which pair $\left(a,b\right)$ makes $f$ continuous at $x=1$?

Let $f(x)=\{\begin{array}{ll}{x}^2-k& x\le -4\\ -2x+2k& x>-4\end{array}$. Which equation must hold for $f$ to be continuous at $x=-4$?

Let $g(x)=\{\begin{array}{ll}\frac{x^2-25}{x+5}& x\ne -5\\ c& x=-5\end{array}$. For what value of $c$ is $g$ continuous at $x=-5$?

Let $g(x)=\{\begin{array}{ll}\frac{x^2-36}{x-6}& x\ne 6\\ c& x=6\end{array}$. For what value of $c$ is $g$ continuous at $x=6$?

Let $u(x)=\{\begin{array}{ll}-4x+k& x<2\\ x^2-5& x\ge 2\end{array}$. For what value of $k$ is $u$ continuous at $x=2$?

Let $f(x)=\{\begin{array}{ll}{x}^2-k& x\le 2\\ -6x+2k& x>2\end{array}$. Which equation must hold for $f$ to be continuous at $x=2$?

Let $h(x)=\{\begin{array}{ll}\frac{1}{x+8}& x<-8\\ k& x\ge -8\end{array}$. For what value of $k$ is $h$ continuous at $x=-8$?

Let $f(x)=\{\begin{array}{ll}ax+b& x<1\\ 7& x=1\\ 5ax-9b& x>1\end{array}$. Which pair $\left(a,b\right)$ makes $f$ continuous at $x=1$?