Question

analyze the graph f(x)=(x-2)^3(x-3)^2(x-4)

a)end behavior: find the power function that the graph of f resembles for large values of absolute value of x

Answer 1

triple root at x=2
double root at x=3
root at x=4

the graph crosses the x-axis at x=2 and x=4, but is tangent at x=3

for huge values of x, the graph resembles that of the highest power: x^6
f(x) -> +infinity for large x, plus or minus.

enter the function at wolframalpha.com to see the graph