Question

Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the y-intercept, x-intercepts, and the shape of the graph.

Answer 1

Answer:  x-intercept is (5,0),(4,0) and (9,0)    and y-intercept is (0,-180)  

Explanation:

x-intercept is the point where graph intersects the x-axis.Hence, to find x-intercept, plug y=0 in the given function

y-intercept is the point where graph intersect the y-axis.Hence, to find y-intercept, plug x=0 in the given function.

here in given function we have leading coefficient is 1 and degree is 3

So, for end behaviour it is the case of odd degree and positive leading coefficient so

$x\rightarrow -\infty$           $f(x)\rightarrow -\infty$

$x\rightarrow \infty$              $f(x)\rightarrow -\infty$

Answer 2

y-intercept : (0, -180)
x-intercepts : (9, 0), (5, 0), (4, 0)
It is hard to describe the shape of the graph, it will be easier for you to graph it and see it yourself