How do I find out what is the end behavior diagram for πx^7-x^5-5x+6

1 answer:

3 0

It is really simple, although maybe not completely intuitive...however the end behavior of any function can be seen as the value that the function would approach as if only the highest powered variable existed...

In this case the end behavior will be that of πx^7 as x→±oo

Since this is an odd power, and has a positive coefficient, π, the end behavior will be:

f(x)→-oo as x→-oo and f(x)→+oo as x→+oo

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Find the coordinates of the circumcenter for triangle DEF with coordinates D(1,3) E(8,3) and F(1,-5) show your work

nikklg [1K]

One leg is horizontal, on the line y=3. Another leg is vertical, on the line x=1. The point where these intersect, D(1, 3) is the vertex of a right angle. Any right triangle inscribed in a circle has its hypotenuse as the diameter of the circle.

Since the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse: ((8, 3) + (1, -5))/2 = (4.5, -1).