SOLUTION: Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3 a.) Find the x- and y- intercepts of f. b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this

Algebra ->  Functions -> SOLUTION: Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3 a.) Find the x- and y- intercepts of f. b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this       Log On


   

Question 57793: Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3
a.) Find the x- and y- intercepts of f.
b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this without graphing f?
c.) What power function does f resemble for very large values of |x|?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given f(x)=(x+1)^2(x-1)(x+2)(x+4)^3
a.) Find the x- and y- intercepts of f.
For y-int let x=0, then y=1^2*-1*2*4^3=-48
For x-int: x=-1 of multiplicity 2; 1 mult 1; -2 mult 1; -4 mult 3
b.) Determine whether the graph touches or crosses the x-axis at each x-intercept. How do you do this without graphing f?
If the multiplicity is even the curve touches but does not cross the x-axis
at that x value; if the multiplicity is odd the graph passes through the
x axis at that x value.
c.) What power function does f resemble for very large values of |x|?
f(x)=x^7
Cheers,
Stan H.