Use the graph and the function to find the following. a) Find $\lim _{x \rightarrow 0} k(x)$. b) Find $k(0)$. c) Is $k$ continuous at $x=0$ ?

Step 1 ：Let's consider a function \(k(x) = x^2\).

Step 2 ：To find the limit of \(k(x)\) as \(x\) approaches 0, we evaluate the function from both the left and right of 0. If the two values are equal, then that is the limit. For the function \(k(x) = x^2\), the limit as \(x\) approaches 0 is 0.

Step 3 ：To find the value of \(k(x)\) at \(x = 0\), we substitute 0 into the function. So, \(k(0) = (0)^2 = 0\).

Step 4 ：A function is continuous at a point if the limit as \(x\) approaches that point is equal to the value of the function at that point. Therefore, since the limit of \(k(x)\) as \(x\) approaches 0 is 0 and the value of \(k(0)\) is also 0, the function \(k(x)\) is continuous at \(x = 0\).

Step 5 ：Final Answer: a) The limit of \(k(x)\) as \(x\) approaches 0 is \(\boxed{0}\). b) The value of \(k(0)\) is \(\boxed{0}\). c) The function \(k\) is \(\boxed{\text{continuous}}\) at \(x = 0\).