©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
1. (16 points) If f (x) = log 2 (x + 4) − 3 , then provide the following. (If there are none, write
NONE in the blank provided.)
a) domain (in interval notation): _____________
b) range (in interval notation):_______________
c) coordinates of the anchor point __________
d) coordinates of the y-intercept ____________
e) coordinates of the x-intercept(s) _________
f)
equation of the horizontal asymptote ___________
g) equation of the vertical asymptote _______________
h) sketch the graph f (x) = log 2 (x + 4) − 3 in the space above
2. (5 points) sin (12! ) = 0.2 . If the measure of an obtuse angle is θ , and sin θ = 0.2 , then θ =
a) arcsin θ
b) arccosθ
d) 168!
c) 0.8
3
e) None of these
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
3. (14 points) If g(x) = e x − 3 , then provide the following. (If there are none, write NONE in the
blank provided.)
a) domain (in interval notation): _____________
b) range (in interval notation):_______________
c) coordinates of the y-intercept ___________
d) coordinates of the x-intercept(s) _________
e) equation of the horizontal asymptote ______
f) equation of the vertical asymptote ________
g) sketch the graph of g(x) = e x − 3 in the space above
4. (3 points) Write the equation of a circle with center at ( 2, − 3) and a radius of 6 .
__________________________________________________________________________
4
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
5. (18 points) Given h(x) = 2sin ( 4x ) + 1 then provide the following. (If there are none, write
NONE in the blank provided.)
a) domain (in interval notation): __________
b) range (in interval notation):____________
c) coordinates of the y-intercept ____________
d) period ___________________________
e) graph h(x) = 2sin ( 4x ) + 1 on [0, 2π ]
f) coordinates of the x-intercept(s) on [0, 2π ] ________________________________
5
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
6. (8 points) The graph of this equation is a circle: 4x 2 + 4y 2 − 8x + 12y − 7 = 0
Put this equation into standard form: _______________________________________
7. (5 points) Simplify sin x tan x + cos x
a) sin x
b) cos x
c) tan x
d) sec x
6
e) None of these
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
8. (6 points) Seaborgium-266 has a half-life of 30 seconds. Determine its exponential decay
model.
9. (6 points) A team of scientists are studying a certain lab specimen. They start with 20
individuals and find that the population triples every 7 weeks, write an equation predicts the
population of the specimen at any time t (where t is given in weeks).
7
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2014
10 (20 points) Calculate, if possible. If not possible, write UNDEFINED.
a)
log 6 9 + log 6 4 =
c)
ln e3 =
e)
g)
______________!
!
b) log(1) = ______________!
!
!
d)
⎛ 1⎞
log 3 ⎜ ⎟ = __________________!!
⎝ 9⎠
!
f)
!
log16
h)
log 2
!
j) log − 10 = ____________
______________! !
log 600 − log 6
= ________________!
i) log1000 = ____________!
!
!
8
eln 2 = ______________!
⎛ 1⎞
log 9 ⎜ ⎟ =
⎝ 3⎠
(
______________
= ____________
)
©Fry Texas A&M University
!
Math 150 Precalculus
11. (5 points) Circle one.
log x
log(x + 2)
a) TRUE or FALSE !
!
log x − log(x + 2) =
b) TRUE or FALSE !
!
log(x + 6) = log x + log 6
c) TRUE or FALSE !
!
e ≈ 2.141
d) TRUE or FALSE !
!
log x 3 = 3log x
e) TRUE or FALSE !
!
log 50 = log 5 + 1
9
Spring 2014