Final answer:
To sketch the graph, address each condition one by one: a. Removable discontinuity at x = -1, b. p(-1) = 3, c. Absolute maximum of 3, d. lim(x→0-) p(x) = 0, e. Relative minimum at x = -3, f. lim(x→[infinity]) p(x) = 0.
Step-by-step explanation:
To sketch a graph of a function p(x) satisfying the given conditions, we can start by addressing each condition one by one.
a. A removable discontinuity at x = -1 means that there is a hole in the graph of the function at x = -1. We can represent this by drawing an open circle at x = -1 on the graph.
b. Since p(-1) = 3, we can plot the point (-1, 3) on the graph.
c. To have an absolute maximum of 3, the graph of p(x) should have a peak at some point. We can add a local maximum at any point we choose, as long as its y-coordinate is 3.
d. To have lim(x→0-) p(x) = 0, we can ensure that the graph approaches the x-axis from the left side as x approaches 0.
e. To have a relative minimum at x = -3, we can add a local minimum at that point.
f. To have lim(x→[infinity]) p(x) = 0, the graph needs to approach the x-axis as x goes to positive infinity.
By incorporating all these conditions, we can sketch the final graph of p(x).