Question

Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.

Answer 1

for the shape: they're probably wanting end behavior + number of turns

since the highest exponent is odd and the leading coefficient is positive, it goes to -infinity as x goes to -infinity and to + infinity as x goes to + infinity

number of turns = highest exponent - 1 = 2 so 2 turns

Answer 2

for the y-intercept, plug in x = 0 and find f(x)

Answer 3

for the x-intercepts, this is kind of tricky since you'll have to use the rational root theorem, and there are a LOT of possible roots for this one (there are a lot of factors of 210) so to be generous I went ahead and graphed it and the x-intercepts are 5,6,7