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Rationals
simplifying rationals & finding domains
Put it in words
100
A rational number can be written as a quotient of two integers, or in other words as a...
What is a fraction
100
the domain of the quotient of x and 2
What is a) the set of all real numbers, or b) in interval notation (minus infinity, infinity)
100
Ex 7 p. 438: Given a function C(x) = (2.6x +10,000)/x where C(x) representsthe cost per disc of prssing x compact discs,find the cost per disc for pressing 100 compact discs
What is $102.60
200
An expression that can be written as the quotient of two polynomials is called this kind of expression
What is a rational expression
200
What is the domain of the function f(x) = (7x - 2) divided by the product of (7x-2)(x+3)
What is x not equal to 2/7 and x not equal to negative3 (in other words in interval notation (-infinity, -3) U (-3, 2/7) U(2/7,infinity)
200
p. 442 #62: The total revenue R(x) from the sale of a popular music compact disc is approximately given by the function R(x) = (150 x^2) divided by (x ^2 + 3) Where x is the number of years since the CD has been released and revenue R is in millions of dollars. The total revenue generated by the end of the first year is
What is $37.5 million
300
If a rational expression has a denominator of 0 then it is
What is UNDEFINED
300
The rational function in simplest form: The quotient of (9x^2 + 13x +4) and (8x^2 + x - 7)
What is the quotient of (9x+4) and (8x - 7 ) (see p. 435 ex 2b)
300
in your own words, describe how to simplify a rational expression
What is : make sure the numerator and the denominator are completely factored! and then divided out any common factors to the numerator & denominator) Remember that 2/2 = x/x = (x+2)/(x+2) = 1 AND remember to check for domain!!!
400
The set of all x-coordinates in a rectangular coordinate system is called ... For a Rational function, this would be all the values that exclude any x value that makes the rational expression become undefined.
What is the domain
400
p. 436 ex 4: Simplify the quotient (18 - 2x^2) and (x^2 - 2x - 3)
What is - 2 (x+3) / (x+1)
400
In your own words, explain how to find the domain of a rational function
What is : all real numbers EXCEPT those that make the denominator 0! So check the denominator and if it has no variables the domain is all real numbers. If it has variables, then be sure to set the denominator to NOT equal 0, and factor if appropriate, and set equation(s) to solve for x values that will make this 0. These are the restrictions. The interval notation will exclude these restrictions. example x not equal 1 is (-infinity,1)U(1,infinity)
500
The domain of (x -2) divided by (x +1)
What is x NOT equal to -1 (in words, minus one) Or in interval notation (-infinity, -1) U (-1, infinity)
500
Simplify the rational expression (3-x) / (x-3)
What is MINUS ONE (in other words -1)
500
Study strategies: List THREE Pitfalls andTHREE tips for success for exam preparation!
What is (varies) :)