MTH 1280 College Algebra

Homework, Week #7 – over Lessons 14, 15, and 16, and Workshop 7 Due at the start of class 10/10/14 Name: ______________________

As you do these problems, show your work clearly!

#1. A linear function has a graph that passes through the points

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−1,6( ) and

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5,4( ) ; find its equation, and express it using Function Notation, with function variable

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g and input variable x.

#2. Find the equation of linear function

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h that passes through the point

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−3,8( ) and is perpendicular to

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f x( ) = 2 3 x + 1 ; express it

using Function Notation.

#3. Evaluate each of the rational number logarithms below. To do so, you must use the Definition of Logarithm, the properties of logarithms, and/or the Laws of Logarithms. However, do not use your calculator! (Answers given showing insufficient work will receive little or no credit; consult with your teacher if you are uncertain what constitutes “sufficient work.”)

a)

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log6 4( ) + log6 54( ) b)

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log5 1

253



  



   c)

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log2 5( )−log2 40( )

#4. Given the quadratic function

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q defined by the equation

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q x( ) =−4x2 + 24 x + 80 , complete the square to put the function into standard form. Then write down the vertex, domain, range, interval of increase, and interval of decrease.

completed square form (use Function Notation): ________________________ vertex: __________

Domain(

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q)

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≈ __________________ Range(

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q)

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≈ __________________

Interval of increase of

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q: __________________ Interval of decrease of

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q: __________________

#5. Given the polynomial function

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p defined by the equation

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p x( ) =−x3 − x2 + 8x + 12 , follow the directions and answer the questions below. (To save you time, here is the function, in factored form:

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p x( ) = 3− x( ) x + 2( ) 2

.)

a) BehaviorToTheLeft(

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p) = _________________________ b) BehaviorToTheRight(

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p) = _________________________

c) List the coordinates of the intercepts: ______________________________

d) SetOfZeros(

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p) = _________________ e) Degree(

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p) = _________________

f) Create an interval chart (as we did in class) to determine the intervals for which the function is positive or negative.

y

i) Graph the function by hand, using your work above; remember to scale the axes.

x

h) SubdomainWhereBelowTheX-Axis(

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p) = ________________

g) SubdomainWhereAboveTheX-Axis(

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p) = ________________