Consider the polynomial function p(x) = -5x^6-3x^5+4x^2+6x What is the end behavior of the graph of p?

The correct answer is C.  As x approaches ±∞, p(x) approaches -∞

Step-by-step explanation:

The easiest way to see this is to consider the term with the largest power of x.  In this case that's the first term -5x⁶.  Because the exponent is an even number, the function will ultimately move in the same direction as x approaches infinity.  If the exponent was odd, like -5x⁷, then they'd be moving in opposite directions.

The next thing to consider is the coefficient.  If the coefficient is positive, then the left side of the curve goes downward, and the right side goes either downward or upward depending on the exponent.  If the coefficient is negative, then the left side goes upward, and the right side goes upward or downward depending on the coefficient.

In this case, we have a negative coefficient, so the left side goes downward, and an even power, so the right side goes the same way as the left side.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.