3.1 Graphs of Polynomial Functions. Pg. 150 #25 – 32 all, Pg. 161 #1 – 4, 23 – 33 odd, 35 – 37 #2 [-4, 5] by [-10, 100] #5 [-5, 30] by [-5,000, 5,000] #8 [-4, 6] by [-400, 100] #11 Zeros = min = (2, 0), (5, 0); max = (3.5, 2.25) #14 No zeros; no local max; min = (1.5, 5.5)
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A function is considered continuous on a given interval if it is possible to trace it on that given interval without lifting up your pencil.
If the function fails to be continuous, it is discontinuous.
All polynomial functions are continuous!!
Points of Discontinuity
Determine if the following functions are continuous or discontinuous. If they are discontinuous, state why.
Intermediate Value Theorem (Property)
The cool thing about polynomials… they are continuous EVERYWHERE!!!
Looking at Graphs
For each of the following graphs:
State the local extrema
State the zeros
State the intervals of increasing and decreasing