Midterm Examination

Midterm Examination.

1.       Question Details                                                                                                  StitzCA3 1.4.062. [3114682]     –

Find the (implied) domain of the function. (Enter your answer using interval notation.)

   w − 2  

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u(w) =  5 −    w

2.       Question Details                                                                                                  StitzCA3 2.1.029. [1848968]     –

Carl can stuff 6 envelopes per minute. Find a linear function E that represents the total number of envelopes Carl can stuff after t hours, assuming he doesn’t take any breaks.

E(t) =                          , t ≥ 0

3.       Question Details                                                                                          StitzCA3 2.2.025.part5. [3116225]     –

Consider the following function.

f(x) = −4|x|

From the graph, list the intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If the answer cannot be expressed as an interval, enter EMPTY or ∅.)




4.       Question Details                                                                                                  StitzCA3 1.6.023. [1847380]     –

Analytically determine if the following function is even, odd or neither.

f(x) = 6   even


  both even and odd neither

5.       Question Details                                                                                                  StitzCA3 2.5.005. [1849003]     –

On New Year’s Day, I (Jeff) started weighing myself every morning in order to have an interesting data set for this section of the book. (The professionals in the field of weight management strongly discourage weighing yourself every day. When you focus on the number and not overall health, you tend to lose sight of your objectives. I was making a noble sacrifice for science, but you should not try this at home.) The whole chart would be too big to put into the book neatly, so I’ve decided to give only a small portion of the data to you. This then becomes a Civics lesson in honesty, as you shall soon see. There are two charts given below. One has my weight for the first eight Thursdays of the year (January 1, 2009 was a Thursday and we’ll count it as Day 1.) and the other has my weight for the first 10 Saturdays of the year.

Day # x

(Thursday)          1        8       15       22       29       36       43       50

My weight y

in pounds     238.2  237.0  235.6  234.4  233.0  233.8  232.8  232.0

Day # x

(Saturday)          3       10       17       24       31       38       45       52       59       66

My weight y

in pounds     238.4  235.8  235.0  234.2  236.2  236.2  235.2  233.2  236.8  238.2

(a) Find the least squares line for the Thursday data. (Round the slope and the y-intercept to two decimal places.)

y(x) =

Is it a good fit?



(b) Find the least squares line for the Saturday data. (Round the slope to six decimal places and the y

intercept to two decimal places.)

y(x) =

Is it a good fit?



(c) Use Quadratic Regression to find a parabola which models the Saturday data. (Round your answer for the x2 coefficient to three decimal places and your answers for the x coefficient and constant term to two

decimal places.)

y(x) =

Is it a good fit?



6.       Question Details                                                                                                  StitzCA3 1.7.041. [1849356]     –

The complete graph of

a(x) = f(x+ 1)

y = f(x)

is given below. Use it to graph the following function.


Page  3  of  5

7.       Question Details                                                                                            StitzCA3 1.1.026.cap. [1848694]     –

Consider the following pair of points.

 23 ,  2

,     −  22 , −  13

5    5             5        5

Part 1 – Distance

Find the distance d between the two points.

d =

Part 2 – Midpoint

Find the midpoint M of the line segment connecting the two points.

M(x, y) =

Midterm Examination

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