Math 131 Fall 2015
Test 1B
Name:
On my honor, as an Aggie, I have neither given nor received
unauthorized aid on this academic work.
Signature:
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.
Use the graph of the function f below to answer questions 1-4
1.
(2 points) f (x) is countinuous at x = 0.
True
2.
(2 points) Limx→−1/2 exists.
True
3.
False
(2 points) f (x) is decreasing on the interval (1,3).
True
4.
False
False
(2 points) f (x) is continuous from the left at x = 1.
True
False
5.
(6 points) Express g(x) = 3f (2 − x) as a transformation of the graph of f (x).
(a) First reflected about the y-axis. Then vertically stretched by a factor of 3. Then shifted
right 2.
(b) First reflected about the x-axis. Then vertically stretched by a factor of 3. Then shifted left
2.
(c) First reflected about the y-axis. Then vertically stretched by a factor of 3. Then shifted left
2.
(d) First reflected about the x-axis. Then vertically stretched by a factor of 3. Then shifted
right 2.
(e) None of the above
6.
(6 points) Solve for x in terms of a. ex+1 e2x−1 = a
(a) x = ln(a/3)
p
(b) x = ln(a) + 3
(c) x = ln(a)
p
(d) x = ln(a) − 3
(e) x = ln(a)
3
7.
(8 points) Solve for x in terms of a, ln(2 − x)− ln(x + 3) = a
8.
(8 points) Evaluate the limit of f (x) =
(a) Limx→1 f (x) =
(b) Limx→∞ f (x) =
x2 +4x−5
x2 −1
(be sure to show the algebraic steps)
9.
(8 points) Paul travels along a road according to the distance function, d(t) = 2t2 − 3t + 7.
(a) Calculate his average velocity on the interval [1, 3] (Be sure to show your work).
(b) Approximate his instantaneous velocity at t = 3 (Show the table of values your calculator
gives you)
10.
(12 points) Give f (x) =
(a) What is (f ◦ g)(0)?
x+2
x−3
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 240 bacteria. Two hours later Sally counts 2160 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 and round to whole number).
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
18 48 75 92 114 145 167 189
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) =
14.
(10 points) Sketch a graph of,

if x ≤ −2
 2x + 3
f (x) = (x + 1)2 − 1 if − 2 < x ≤ 0

−2
if x > 0
p
3
ln(x − 2) + 3.