Since we want to find the value of k where the limit exists, set both equations equal to each other. Then substitute x = -1 in for each equation to find k.
[tex]kx - 3 = {x}^{2} + k[/tex]
1. Set both equations equal.
[tex] - k - 3 = 1 + k[/tex]
2. Substitute x = -1.
[tex] - 3 = 1 + 2k[/tex]
3. Solve for k by adding k to both sides. Continue the process of solving the equation.
[tex] - 4 = 2k[/tex]
[tex]k = - 2[/tex]
Thus, k = -2. Check by graphing the function.
