Answered

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Use the equation of the polynomial function f(x)=−4x4−x to complete the following.(a) State the degree and the leading coefficient.(b) Describe the end behavior of the graph of the function.(c) Support your answer by graphing the function.

Use The Equation Of The Polynomial Function Fx4x4x To Complete The Followinga State The Degree And The Leading Coefficientb Describe The End Behavior Of The Gra class=

Sagot :

Answer

a) Degree of this polynomial = 4

Leading coefficient = -4

b) The end behavior is that the two ends of the graph of the function will head downwards indicating that the value of the function tends towards negative infinity as the values of x get too large or too small.

The curve opens down to the right because the leading coefficient is negative. Because the polynomial is quartic the graph has end behaviors in the same direction and opens down to the left.

c) The graph of the functionis presented below

Explanation

The polynomial is given as

f(x) = -4x⁴ - x

a) Degree and leading coefficient

The degree of a polynomial is the greatest power of x in the polynomial.

For this question, the greatest power of x is 4.

Degree of this polynomial = 4

The leading coefficient is the coefficient of the greatest power of x in the polynomial.

For this question, the coefficient of x⁴ is -4

Leading coefficient = -4

b) The end behavior

End behavior is obtained by getting f(x) for the lowest possible values of x, that is, x → -∞ and for the greatest possible values of x, that is, x → ∞

So, all of these depends on the degree of the polynomial and the leading coefficient of the polynomial.

The odd-degree polynomials have ends that head off in opposite directions.

If they start up and go down, they are negative leading coefficient polynomials.

If they start down and go up, they are positive leading coefficient polynomials.

The even-degree polynomials have ends that head off in the same direction.

If the ends both head up, then it has a positive leading coefficient.

But if both ends head down, then it has a negative leading coefficient.

For this question, we have an even degree polynomial with a negative leading coefficient, hence, the two ends will head downwards in the same direction.

The end behavior is that the two ends of the graph of the function will head downwards indicating that the value of the function tends towards negative infinity as the values of x get too large or too small.

Part c

The graph of this function is presented above under 'Answer'.

Hope this Helps!!!

View image KhushW368676
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