Question

Describe the graph of this function

Answer 1

X3−18x2+107x−210
So this is a cubic function that needs to be factored:
what goes into 210? 7×30
and what goes into 30? 5×6
So double check the b & c values, but it should factor into (x-5)(x-6)(x-7)
So the roots/solutions (or x-intercepts) are where those 3 = 0, so x = 5, 6, and 7
For y-intercept set x = 0:
${x}^{3} - 18 {x}^{2} + 107x - 210\\ \: 0 - 0 + 0 - 210 = - 210 \\ y = - 210$
graph starts low in 3rd quadrant, then crosses at y=-210 into 4th quadrant rising up to cross x-axis at 5, quickly back down at six, then up into 1st quadrant at 7

Answer 2

Describe the two functions f and g , using the terms increasing, decreasing, maxima and minima. The graph of f is periodic. ... It has a maximum value of 1 and a minimum value of − , and it attains these maxima and minima many times. The upper bound of the function is 1 and the lower bound is − .