Consider the following polynomial functions:
- $f(x)=4 x^{2}+3 x^{6}-8$
- $g(x)=7 x^{7}-x+3 x^{4}+1$
- $h(x)=3 x^{6}+3 x-5$
- $j(x)=1-12 x^{10}$
- $k(x)=10 x^{18}-1$
a. Which of the following polynomial function definitions from above are written in standard form? Select all that apply.
b. Determine the degree of each of these polynomial functions.
- Degree of $f$ :
- Degree of $g$ :
- Degree of $h$ :
Degree of $j$ :
Degree of $k$ :

Step 1 ：First, we need to identify which of the given polynomial functions are written in standard form. The standard form of a polynomial function starts with the term with the highest degree and follows in descending order. From the given functions, $f(x)$ is not in standard form because the term with the highest degree (which is $3x^6$) is not the first term. Therefore, the polynomial functions in standard form are $g(x)$, $h(x)$, $j(x)$, and $k(x)$.

Step 2 ：Next, we need to determine the degree of each polynomial function. The degree of a polynomial function is the highest power of the variable in the function. Therefore, the degree of $f(x)$ is 6, the degree of $g(x)$ is 7, the degree of $h(x)$ is 6, the degree of $j(x)$ is 10, and the degree of $k(x)$ is 18.

Step 3 ：\(\boxed{\text{a. The polynomial functions written in standard form are } g(x), h(x), j(x), \text{ and } k(x).}\)

Step 4 ：\(\boxed{\text{b. The degrees of the polynomial functions are:}}\)

Step 5 ：\(\boxed{\text{Degree of } f : 6}\)

Step 6 ：\(\boxed{\text{Degree of } g : 7}\)

Step 7 ：\(\boxed{\text{Degree of } h : 6}\)

Step 8 ：\(\boxed{\text{Degree of } j : 10}\)

Step 9 ：\(\boxed{\text{Degree of } k : 18}\)