Question

Identify whether the function graphed has an odd or even degree and a positive or negative leading coefficient.

Answer 1

Answer: odd and positive

How to find number of degrees: Count the number of turns and add one. In this case you have 4 curves, so 4+1= 5.

How to find leading coefficient: look at the RIGHT side of the graph, the arrow is going towards positive infinity, thus making the leading coefficient positive.

Answer 2

Coefficient if Positive and the degree of f(x) is Odd.

According to the question,

Let y = f(x) be the polynomial whose graph is shown in the question.

So,

• $f(x) = a_n \ x^n+............+a_0$

From the graph,

• $\lim_{x \to \infty} f(x) = \infty$
• $\lim_{x \to -\infty} f(x) = -\infty$

Then the leading coefficient $a_n$ will be positive.

Now,

From the graph, the equation $f(x) =0$ has 3 real roots.

As the complex roots occur in pairs, it follows that the degree of $f(x) = 3+2k$, for some integer k.

Thus the above answer is correct.

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