Consider the following polynomial functions: - $f(x)=4 x^{2}+4 x^{6}-8$ - $g(x)=7 x^{8}-x+3 x^{4}+1$ - $h(x)=4 x^{5}+3 x-5$ - $j(x)=1-13 x^{11}$ - $k(x)=14 x^{13}-1$ a. Which of the following polynomial function definitions from above are written in standard form? Select all that apply.

Step 1 ：Consider the following polynomial functions: \(f(x)=4 x^{2}+4 x^{6}-8\), \(g(x)=7 x^{8}-x+3 x^{4}+1\), \(h(x)=4 x^{5}+3 x-5\), \(j(x)=1-13 x^{11}\), \(k(x)=14 x^{13}-1\)

Step 2 ：The standard form of a polynomial function is written with the terms in descending order by degree. That is, the term with the highest degree is written first, followed by the term with the next highest degree, and so on, until the term with the lowest degree (the constant term) is written last.

Step 3 ：Checking each function one by one:

Step 4 ：\(f(x)=4 x^{2}+4 x^{6}-8\): This function is not in standard form because the terms are not in descending order by degree. The term with the highest degree (\(4x^6\)) should be written first.

Step 5 ：\(g(x)=7 x^{8}-x+3 x^{4}+1\): This function is not in standard form because the terms are not in descending order by degree. The term with the highest degree (\(7x^8\)) is written first, but the next term is \(-x\), which is not the term with the next highest degree.

Step 6 ：\(h(x)=4 x^{5}+3 x-5\): This function is not in standard form because the terms are not in descending order by degree. The term with the highest degree (\(4x^5\)) is written first, but the next term is \(3x\), which is not the term with the next highest degree.

Step 7 ：\(j(x)=1-13 x^{11}\): This function is not in standard form because the terms are not in descending order by degree. The term with the highest degree (\(-13x^{11}\)) should be written first.

Step 8 ：\(k(x)=14 x^{13}-1\): This function is in standard form because the terms are in descending order by degree. The term with the highest degree (\(14x^{13}\)) is written first, followed by the constant term.

Step 9 ：Final Answer: The only polynomial function definition from above that is written in standard form is \(\boxed{k(x)=14 x^{13}-1}\)