Consider the polynomial function p(x)= -9x^9 +6x^6 -3x^3 +1.What is the end behavior of the graph of p?

Answer:

The end behavior of the graph of p is:

f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞

Step-by-step explanation:

Given the polynomial function

Since the leading term of the polynomial (the term in a polynomial that contains the highest power of the variable) is -9x⁹, then the degree is 9 i.e. odd, and the leading coefficient is -9, i.e. negative.

This means that f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞

The graph is also attached below.

Thus, the end behavior of the graph of p is:

f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞

The graph of p(x) will start from the bottom-left and extend towards the top-right of the coordinate plane.

Use the concept of a graph defined as:

Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.

The given polynomial is:

Since we know that,

The end behaviour of the graph of p(x) can be determined by looking at the leading term, which in this case is .

Here, the leading term has an odd degree and a negative coefficient,

the end behaviour of the graph will be as follows:

As x approaches negative infinity, the graph of p(x) will decrease without bound (goes down indefinitely).

As x approaches positive infinity, the graph of p(x) will increase without bound (goes up indefinitely).

Hence, the graph of p(x) will start from the bottom-left and extend towards the top-right of the coordinate plane.

To learn more about graph of function visit:

brainly.com/question/12934295

#SPJ3