Consider the polynomial function p(x) = 4x^8- 6x^7+ 3x^3- 10.
What is the end behavior of the graph of p?

As x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

And

At negative infinity:

When the variable points to infinity, we only consider the term with the highest exponent. So

Plus infinity, because the exponent is even.

So as x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

At positive infinity:

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.