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. g(x)=7x^5−πx^3+1/5 x

Accepted Answer

Welcome back. I'm so glad you're here. We are given the function F of x equals three X. To the fourth minus pi X squared plus 2/7 X. We are asked to determine whether or not this function is a polynomial and if it is a polynomial, what is its degree? Alright. When we're determining whether a function is a polynomial, we're going to ask ourselves two questions. The first question looks at the exponents of our variables and we ask ourselves are the exponents positive integers. And so our exponents here for our variables are the fourth, the second and then for this X. There is an unwritten one. So 42 and one. Those are all positive numbers and those are all integers for two and one are integers. So we can continue with our second question to determine whether or not this function is a polynomial. The second question is are all of the coefficients and constance real. So our coefficients here are three negative pi and 2/7. We don't have a constant but three negative pi in 2/7. Yes, those are all real numbers. They're not all rational pi is irrational, but it is real. So the two conditions are met. Yes, this is a polynomial. Next we get to take a look at its degree for the degrees. We go back to the exponents, we look for the variable with the highest valued exponents and that here is X. To the fourth and the value of that highest exponents is the value of our degree. So the degree here is for we look at our answer choices and that matches with answer choice a well done, we'll catch 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. g(x)=7x^5−πx^3+1/5 x

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