final pratice exam help please no calculator

Question

Answer 1

20) Observe the graph,

The graph represents a polynomial because it is always a smooth curve; that is, it has no breaks or corners.

Observe the end behavior of the graph, both ends that head off in opposite directions.

So it was odd degree polynomial graph.

 

The graph falls to the right and rises to left.

So the above polynomial odd degree polynomial with a negative leading coefficient.

Therefore, g(x) = - x³ + 4x.

Option (c) is correct.

Comments

The graph falls to the right and rises to left.

So the above polynomial odd degree polynomial with a negative leading coefficient.

Therefore, g(x) = - x³ + 4x.

 

How did you determine that it was a negative leading coefficient but not postive? If it falls down to the right its negative? If its goes up to the right its positive?

 

Also there is 2 answers with negative leading coefficient. Why C but not answer E?

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

If the graph falls to the left and rises to the right , then it was a positive leading coefficient .

If the graph falls to the right and rises to the left , then it was a negative leading coefficient .

 

In this case observe the end behavior of the graph,

So sure that the answer is polynomial odd degree polynomial with a negative leading coefficient.

(c) g(x) = - x³ + 4x

Degree of the polynomial = 3.

3 is odd number.

(E) g(x) = - x⁴ + 4x²

Degree of the polynomial = 4.

4 is even number.

All even degree polynomials are either up on both ends and or down on both ends.

 

Also there are two answers with negative leading coefficient are (c) and (e).

But Option (e) is even degree polynomial.

Option (c) is correct.