Sketch the graph of the function.f(x) = 4 + x    if x < −1x2    if −1 ≤ x < 12 − x    if x ≥ 1 Use the graph to determine the values of a for which lim x → a f(x) does not exist. (Enter your answers as a comma-separated list.)a =

To sketch the graph of the function, we need to consider each piece of the function separately:

1. For x < -1, the function is f(x) = 4 + x. This is a straight line with a slope of 1 and a y-intercept of 4.

2. For -1 ≤ x < 1, the function is f(x) = x^2. This is a parabola that opens upwards with a vertex at the origin (0,0).

3. For x ≥ 1, the function is f(x) = 2 - x. This is a straight line with a slope of -1 and a y-intercept of 2.

Now, to determine the values of a for which the limit as x approaches a of f(x) does not exist, we need to look for discontinuities in the graph.

The function is continuous for all x except possibly at the points where the function definition changes, which are x = -1 and x = 1.

At x = -1, the limit from the left is 4 + (-1) = 3, and the limit from the right is (-1)^2 = 1. Since these are not equal, the limit does not exist at x = -1.

At x = 1, the limit from the left is (1)^2 = 1, and the limit from the right is 2 - 1 = 1. Since these are equal, the limit does exist at x = 1.

So, the only value of a for which the limit does not exist is a = -1.