The function g(x) is defined differently depending on the value of x. Let's analyze the function and determine where it is not continuous.
For a function to be continuous at a specific number, the left-hand limit, right-hand limit, and the value of the function at that number must all be equal.
Let's start by checking if g(x) is continuous at x ≤ 0. Since g(x) is defined as x + 2 for x ≤ 0, we can see that there are no restrictions on the value of x. Therefore, g(x) is continuous for x ≤ 0.
Now let's check if g(x) is continuous at 0 ≤ x ≤ 1. In this interval, g(x) is defined as e^x. Again, there are no restrictions on the value of x, so g(x) is continuous for 0 ≤ x ≤ 1.
To summarize, the function g(x) is continuous for all values of x. There are no numbers at which g is not continuous.
Remember, the definition of continuity states that a function is continuous if the left-hand limit, right-hand limit, and the value of the function at a specific number are equal. In the case of g(x), there are no restrictions on the value of x, making it continuous for all numbers.
I hope this explanation helps you understand the concept of continuity in this context. If you have any further questions, feel free to ask!