# How do you find the degree, leading term, the leading coefficient, the constant term and the end behavior of #f(x)=sqrt3x^17+22.5x^10-pix^7+1/3#?

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See below.

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**Question:**

How do you find

a) the degree,

b) leading term,

c) the leading coefficient,

d) the constant term and

e) the end behavior of

a) **The degree of a polynomial is the degree of the term with the highest power of the variable.**

The highest power present in the polynomial is **17**, so **the degree of the relation, is**

b) **The leading term of a polynomial, in standard form, i.e. written with descending powers of the variable, is the term with the highest degree, so the leading term is**

c) **The leading coefficient is the coefficient of the leading term, i.e. **

d) **The constant term of a polynomial is the term that can be described in one of two ways:**

either the term has no variable factor, or

the term has a variable to the zero power as a factor.

**The constant term is**

e) **The end behavior is found by looking at what the relation does as the variable goes toward # -oo # and # +oo #, which can be expressed as:**

respectively.

**Examining the given relation, one sees that the leading term overpowers the contributions of the other terms**, which contribute little to the value of the relation for large values of x, whether "large and negative" or "large and positive".

To answer this question, then,

**To verify the statement made above about the effect of the effect of large values on the terms, calculate each term for # x = 100 #, to see the effect:**

f(x) has such an interesting graph, I thought it would be good to add it to the display.

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