Question

Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the shape of the graph

Answer 1

one approach is to plot the graph then describe.
look at the intercepts
consider when x is negative and when x is positive

Answer 2

I've just graphed it on desmos.com and have gotten the y and x intercepts,but i'm not sure how to describe the shape of the graph besides including the min and maximums

Answer 3

read all of my response

Answer 4

ok thank you :)

Answer 5

what happens when x is less than 0
what about when x is more than 0
highest exponent 3 should be 3 roots only one value when y = 0 therefore others are complex roots

Answer 6

point of inflection?

Answer 7

so would my description of the graph's shape be something like "the graph begins positive before its max turning point, becoming negative until its min turning point, making it positive until infinity"?

Answer 8

not specific enough
cubic function
explain "begins positive"
indicate the points

Answer 9

when x is <0 the graph is increasing from -infinity to intercept at -1800.

when x >0 the graph is increasing (there is an inflection point at ..) then it continues to increase to positive infinity

can you see the graph from this description?

Answer 10

in my written description I forgot the x-intercept at where y = 0

Answer 11

oh ok now it makes sense after reading my notes and your description. thank you :)

Answer 12

improve on the description cubic function. the left end starts from -infinity when x <0 etc
great!!
all the best
you are welcome