SOLUTION: f(x)=-(x+3)(x-1)²(x+1) Describe or determine the following a.leading term_________ b.behavior of the graph_________ c.x-intercept_________ d. multiplicity of roots___________

Algebra ->  Test -> SOLUTION: f(x)=-(x+3)(x-1)²(x+1) Describe or determine the following a.leading term_________ b.behavior of the graph_________ c.x-intercept_________ d. multiplicity of roots___________      Log On


   

Question 1188405: f(x)=-(x+3)(x-1)²(x+1)
Describe or determine the following
a.leading term_________
b.behavior of the graph_________
c.x-intercept_________
d. multiplicity of roots___________
e.y- intercept________
g. Sketch the graph___________
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=-%28x%2B3%29%28x-1%29%5E2%28x%2B1%29
f%28x%29+=+-x%5E4+-+2+x%5E3+%2B+4+x%5E2+%2B+2+x+-+3
Describe or determine the following
a. leading term____-x%5E4_____
b. behavior of the graph_________
Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is -x%5E4, the degree is 4, i.e. even, and the leading coefficient is -1, i.e. negative.
This means that f%28x%29→-∞ as x→-∞, f%28x%29→-∞ as x→∞.

c. x-intercept_________
0=-%28x%2B3%29%28x-1%29%5E2%28x%2B1%29=> x-intercepts are x=-3, x=-1, x=1

d. multiplicity of roots___________
x=-3 multiplicity 1
x=-1 multiplicity 1
x=1 multiplicity +2
e. y- intercept________
y=-%28x%2B3%29%28x-1%29%5E2%28x%2B1%29 if x=0
y=-%280%2B3%29%280-1%29%5E2%280%2B1%29
y=-3
y- intercept___-3_____
g. Sketch the graph___________


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x%2B3%29%28x-1%29%5E2%28x%2B1%29%29+