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Chapter 4: Q. 5 (page 224)

The domain of every rational function is the

set of all real numbers.

Short Answer

Expert verified

The domain of every rational function is the set of all real numbers except for which denominator will become zero.

so the statement is false.

Step by step solution

01

Step 1. Definition

Rational expression

a rational expression is the quotient of two polynomial expressions where the denominator is not equal to zero.

02

Step 2. clarification 

the denominator of the rational expression can not be zero so The domain of rational expression is a set of all real numbers except those value for which denominator will become zero

so the given statement is false

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Most popular questions from this chapter

For a rational functionR, if the degree of the numerator is less than the degree of the denominator, then R is ________.

Make up two polynomial functions, not of the same degree, with the following characteristics: crosses the x-axis at -2, touches the x-axis at 1, and is above the x-axis between -2 and 1. Give your polynomial functions to a fellow classmate and ask for a written critique

The illustration shows the graph of a polynomial function.

(a) Is the degree of the polynomial even or odd?

(b) Is the leading coefficient positive or negative?

(c) Is the function even, odd, or neither?

(d) Why is x2necessarily a factor of the polynomial?

(e) What is the minimum degree of the polynomial?

(f) Formulate five different polynomial functions whose

graphs could look like the one shown. Compare yours to those of other students. What similarities do you see?

What differences?

A rectangular area adjacent to a river is to be fenced in; no fence is needed on the river side. The enclosed area is to be 1000square feet. Fencing for the side parallel to the river is \(5per linear foot, and fencing for the other two sides is \)8per linear foot; the four corner posts are $25apiece. Let x be the length of one of the sides perpendicular to the river.

Part (a): Write a function Cxthat describes the cost of the project.

Part (b): What is the domain of C?

Part (c) Use a graphing utility to graph C=Cx.

Part (d) Find the dimensions of the cheapest enclosure.

Explain the circumstances under which the graph of a rational function will have a hole.
See all solutions

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