Sketch the graph of a function with the given properties. You do not need to find a formula for the function. 


p(0) = 2,lim x→0 p(x) = 0,lim x→2 p(x) does not exist, p(2)=lim x→2^+ p(x)=1

Verified step by step guidance

1. Step 1: Start by plotting the point (0, 2) on the graph, as given by p(0) = 2. This indicates that the function passes through this point.
2. Step 2: Consider the limit as x approaches 0. The limit \( \lim_{x \to 0} p(x) = 0 \) suggests that as x gets very close to 0 from either side, the function value approaches 0. This implies a discontinuity at x = 0 since p(0) = 2.
3. Step 3: Analyze the behavior around x = 2. The limit \( \lim_{x \to 2} p(x) \) does not exist, indicating a discontinuity at x = 2. However, \( \lim_{x \to 2^+} p(x) = 1 \) tells us that as x approaches 2 from the right, the function value approaches 1.
4. Step 4: Plot the point (2, 1) on the graph to represent the right-hand limit at x = 2. Since the limit from the left does not exist, the function may have a jump or an asymptote at x = 2.
5. Step 5: Sketch the graph by connecting the points and considering the limits. The graph should approach 0 as x approaches 0 from either side, jump to 2 at x = 0, and then approach 1 from the right as x approaches 2.