MTH 1280 College Algebra

Homework, Week #8 – over Lesson 17 and Workshop 8 Due at the start of class 10/17/14 Name: ______________________

As you do these problems, show your work clearly!

#1. For the rational function

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f x( ) = x 2 −5x +4

x 2 +2x−24 , determine its domain; write it using Interval Notation.

Domain(

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f ) = _________________________________

#2. For the rational function

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g x( ) = 6 x−2( )

x−2( ) x +7( ) , write the equations of its asymptotes.

Vertical asymptote(s) of

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g : _____________________ Horizontal asymptote(s) of

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g : ___________________

#3. For the rational function

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h x( ) = 2−x( ) x−3( ) 4x x +5( )

, write the equations of its asymptotes.

Vertical asymptote(s) of

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h: _____________________ Horizontal asymptote(s) of

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h: ___________________

#4. For the rational function

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r x( ) = x 3 −2x 2 −8x

x 2 −1 , use algebra to find its zeros and intercepts (remember to write the intercepts as

ordered pairs).

SetOfZeros(

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r ) = __________________________

x-intercept(s): __________________________

y-intercept(s): __________________________

As you do the next two problems, you may wish to refer back to Workshop 8. For each problem, remember to identify the quantities in the problem, set up an equation, solve it, and write a complete sentence to answer the question.

#5. Two cyclists, 48 miles apart, start riding toward each other at the same time. One rides twice as fast as the other. If they meet 2 hours later, at what average speed is each cyclist traveling?

#6. One rectangle is three inches longer than it is wide. A second rectangle is a little bit bigger than the first one; its width is one inch more than the shorter one’s width, and its length is two inches bigger than the shorter one’s length. The sum of the perimeters of the two rectangles is 506 inches. What is the length of the bigger rectangle?