1 pt Let y 7rs 3221249 a What power function does the funct

(1 pt) Let y = 7rs_ 322124-9. (a) What power function does the function above resemble? power function, not just the degree of the power function.) (b) Describe the long-run behavior of the polynomial. Enter INFINITY or -INFINITY for OO or (Enter the entire C0 y goes to y goes to as x -oo.

Solution

1) y = 7x^8 -3221x^4 -9

As x---> y ---> 7x^8

So, power function it resembles : y = 7x^8

2) y = (x-1)^2 (x-6)

X intercept : plug y=0 ; (x-1)^2 (x-6) =0

x1 = 1; x2=1 ; x3 =6

Y intercept: plug x=0

y = (1)(0-6) = -6

End behaviour : x---> +infinity y = + infinty

x -----> - infinity ; y ----> - infinity

3) y = x^3 -5x^2 -6x

= x( x^2 -5x -6)

=x(x^2 -6x +x -6) = x(x+1)(X-6)

x1 = -1 ; x2=0 ; x3= 6

x ---> infinty y ----> infinty

x ----> - infinty ; y ----> -infinity