Math 131 Fall 2015
Test 1A
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You may use your calculator for all problems on the test but be sure to read each problem carefully. Some problems ask you to show some algebraic steps.

f
1.
( 2 points ) f ( x ) is countinuous at x = 4.
True False
2.
( 2 points ) Lim x → 4 does not exist.
True False
3.
( 2 points ) f ( x ) is decreasing on the interval (-4,2).
True False
4.
( 2 points ) f ( x ) is continuous from the left at x = 0.
True False

5.
( 6 points ) Express g ( x ) = − f (3 x ) + 2 as a transformation of the graph of f ( x ).
(a) A shift up 2. Then a reflection abou the y -axis. Then a horizontal stretch by a factor of 3.
(b) A shift up by 2. Then a reflection abou the x -axis. Then a horizontal shrink by a factor of
3.
(c) A shift up 2. Then a reflection about the x -axis. Then a horizontal shrink by a factor of
1/3.
(d) A reflection about the y -axis. Then a horizontal stretch by 3. Then a shift up by a factor of
2.
(e) A reflection about the x -axis. Then a horizontal shrink by a factor of 1/3. Then a shift up by a factor of 2.
6.
( 6 points ) Solve for x in terms of a .
e x +2 e x − 2 = a
(a) x = ln( a ).
(b) x = ln( a )
2
(c) x = ln( a/ 2)
(d)
(e) x x
=
= p ln( a ) − 4 p ln( a ) + 4
7.
( 8 points ) Solve for x in terms of a , ln( x + 7) − ln( x − 1) = a
8.
( 8 points ) Evaluate the limit of f ( x ) = x
2
+6 x − 7 x
2 − 1
(be sure to show the algebraic steps)
(a) Lim x → 1 f ( x ) =
(b) Lim x →∞ f ( x ) =

9.
( 8 points ) Paul travels along a road according to the distance function, d ( t ) = 2 t
2 − 3 t + 7.
(a) Calculate his average velocity on the interval [2 , 4] (Be sure to show your work).
(b) Approximate his instantaneous velocity at t = 4 (Write the table of values you used to find the approximation)
10.
( 12 points ) Give f ( x ) = x − 2 x +3
(a) What is ( f ◦ g )(2)?
and g ( x ) = x +1 x − 1
,
(b) Find ( g ◦ f )( x ) and state its domain.
11.
( 12 points ) A bacteria sample grows exponentially in the lab. Sally, the lab tech, checks the sample after one hour and counts 480 bacteria. Two hours later Sally counts 7680 bacteria.
Find a model for this bacteria growth and use it to predict the number of bacteria after 4.5
hours. (Be sure to show your algebra).

12.
( 10 points ) Jenny is an amateur entomologist. She counts the number of chirps a cricket makes based on the temperature outside. Over a period of time she collected the following data,
Chirps 19 47 73 95 117 142 168 190
Temperature 40 45 50 55 60 65 70 75
Find a linear model, C ( T ) for her data and use it to predict how many times this cricket would chirp at 57 degrees (round to 3 decimal places).
13.
( 12 points ) Find the inverse function for f ( x ) = p ln( x + 1) − 2.
14.
( 10 points ) Sketch a graph of, f ( x ) =
 2 x + 3

( x − 2) 2 if x ≤ 0
+ 1 if 0 < x < 4
 5 if x ≥ 4