In Exercises 1–10, determine which functions are polynomial funct...

Question

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3

Accepted Answer

Welcome back. I'm so glad you're here. We are given the function F of X equals in the numerator X cubed plus eight. All divided by nine. And we are asked to determine whether or not this is a polynomial and if it is what is its degree. Alright, so first we can simplify this a little bit, we can distribute that nine to both of the terms in the numerator. So this would look like well there's a one in front of that X cubed. So this would be 1/9 X cubed plus 8/9. And now to determine if something is a polynomial, we ask ourselves two questions. We ask ourselves are the exponents positive integers and the only exponent here is for this X cubed and yes, this three is a positive integer. So now we ask ourselves the second question and that is are all the coefficients and constance real numbers. So we've got to we've got a coefficient this 1/9 and we've got a constant 8/9 and yes, those are both real numbers. 1/9 and 89. 8/9 are real numbers. So yes it is a polynomial and now we get to determine its degree to figure out the degree. We look back at that exponents that we were looking at, we look for the highest valued exponents and that is three. So the degree of our function is the value of the highest valued exponents. The degree is three. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one

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In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=(x^2+7)/3

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