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Chapter 4: Q. 2 (page 234)

If the numerator and the denominator of a rational function have no common factors, the rational function is _______ .

Short Answer

Expert verified

If the numerator and the denominator of a rational function have no common factors, the rational function isin lowest terms.

Step by step solution

01

Step 1 Definition for the rational function:

A rational function is onethat can be written as a polynomial divided by apolynomial.

For example,

fx=x2+1x-1

02

Step 2 If the numerator and the denominator of a rational function have no common factors,

then the rational function is in lowest terms.

The further division of the numerator by its denominator will not be possible.

This is why it is will be in its lowest terms.

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Most popular questions from this chapter

In physics, it is established that the acceleration

due to gravity, g (in meters/sec2), at a height h meters above

sea level is given by

g(h)=3.99×1014(6.374×106+h)2

where6.374×106is the radius of Earth in meters.

(a) What is the acceleration due to gravity at sea level?

(b)

The Willis Tower in Chicago, Illinois, is 443 meters tall.

What is the acceleration due to gravity at the top of the

Willis Tower?

(c) The peak of Mount Everest is 8848 meters above sea

level. What is the acceleration due to gravity on the

peak of Mount Everest?

(d) Find the horizontal asymptote of g(h).

(e) Solve g(h)=0. How do you interpret your answer?

Find the bounds to the zeros of each polynomial function. Use the bounds to obtain a complete graph of f.

f(x)=2x3-x2-11x-6

Solve the inequality algebraically

(x+1)(x+2)(x+3)≤0

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=2x5-x4-x2+1

Find the real zeros of f. Use the real zeros to factor f. f(x)=x4+x3-3x2-x+2
See all solutions

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