Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of f. (If an answer does not exist, enter DNE.)f(x) = 16 − x2      if −4 ≤ x < 03x − 3 if 0 ≤ x ≤ 4absolute maximum     absolute minimum

To sketch the graph of the function f(x) and find the absolute maximum and minimum values, follow these steps:

1. Identify the two pieces of the function: f(x) = 16 - x^2 for -4 ≤ x < 0 and f(x) = 3x - 3 for 0 ≤ x ≤ 4.

2. Sketch the graph of each piece separately.

   For f(x) = 16 - x^2, this is a downward-opening parabola with vertex at (0,16). It is defined for -4 ≤ x < 0.

   For f(x) = 3x - 3, this is a straight line with slope 3 and y-intercept -3. It is defined for 0 ≤ x ≤ 4.

3. Combine the two sketches on the same graph, making sure to only include the parts of each graph that are within the given domain.

4. Identify the absolute maximum and minimum values.

   The absolute maximum value is the highest point on the entire graph. From the sketch, you can see that the absolute maximum is 16, which occurs at x = 0 on the first piece of the function.

   The absolute minimum value is the lowest point on the entire graph. From the sketch, you can see that the absolute minimum is -3, which occurs at x = 0 on the second piece of the function.

So, the absolute maximum is 16 and the absolute minimum is -3.