Question

2.) matching type: 1/2 point for each correct answer (2 points total).
match the polynomial function to its graph.
a. ( y=(x - 1)^2(x + 1) )
b. ( y=-(x + 1)^2(x - 1) )
c. ( y=-(x + 1)^3(x - 1) )
d. ( y=(x - 1)^3(x + 1) )
3.)
use the graph below to answer the drop down question:
drop down: 1 point for answer only
point b is considered a(n)
{absolute/relative}
{minimum, maximum}

Explanation:

Step1: Understand absolute and relative minima

An absolute minimum is the lowest point on the entire graph. A relative minimum is a point that is lower than the points immediately around it but not necessarily the lowest on the whole graph.

Step2: Analyze point B

Looking at the graph, point B is lower than its neighboring points in its local region. But there are other points (like the far - right end approaching negative infinity if we consider the polynomial's end - behavior, but in the visible part, there are lower points than B in the long - run). However, in its local neighborhood (around the small interval where it is located), it is the lowest.

Answer:

relative minimum