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Math Algebra II Blizzard Bag 2014 - 2015 Interpreting functions
1. Brandy is going to pick up her dry cleaning. The distance that she is from home during the
trip can be modeled by a quadratic function, D(x), where D represents the distance Brandy is
from home in miles and x represents the number of minutes that it has been since she left her
house.
How will the graph of the function change when she begins driving back home?
A. the function will change from decreasing to increasing
B. the function will not change, but will continue to increase
C. the function will change from increasing to decreasing
D. the function will not change, but will continue to decrease
2.
Directions: Type the correct answer in each box. Use numerals instead of words.
Two trains leave a train station at the same time. Train A travels 300 miles north inx - 1 hours.
Train B travels 240 miles south in x hours. Train A is travelingy miles per hour faster than train
B. The longest time either train is capable of traveling is 48 hours.
Use the information given above to complete the sentence below.
The domain of the function that models how much faster train A is traveling in terms of the
number of hours train B has been traveling is (
,
)
(
,
].
3. Joise is renting a car for one day. The car rental company charges $22.00 per day plus an
additional fee of $2.00 per mile driven.
Josie's average cost per mile, C(x), can be modeled by a rational function, where x is the
number of miles she drives.
Which of the following best describes Josie's average cost per mile as the number of miles that
she drives increases?
A. There is not enough information to determine Josie's average cost per mile as the
number of miles that she drives increases.
B. Josie's average cost per mile will always be greater than the company's fee per
mile.
C. Josie's average cost per mile will always be equal to the company's fee per mile.
D. Josie's average cost per mile will always be less than the company's fee per mile.
4.
Directions: Type the correct answer in each box. Use numerals instead of words.
The amount of air in a person's lungs t seconds after inhaling is shown below.
The function describing this graph is a transformation of the parent cosine function,y = cos(x).
Find the range, period, and maximum of the transformed function, A(t).
Round to the nearest tenth of a liter, or to the nearest whole second.
The range of the function is best modeled by the interval [
,
The value that best describes the period of the transformed function is
The value that best describes the maximum of the transformed function is
].
seconds.
liters.
5. Andrew is buying a picture frame to hang on the wall of his room. He finds a frame, which
holds a picture with a length two inches longer than its width. The frame also has a wooden
border with a width of three inches. Andrew knows that the width of the largest picture that he
might place in the frame is 12 inches.
The area that the frame will cover on the wall, A(w), can be modeled by a quadratic function,
where w is the width of the picture.
Which of the following graphs correctly models the situation above and gives the correct
domain?
W.
X.
Z.
Y.
A. Y
C. X
B. Z
D. W
6. On the first day of June, tickets go on sale for a popular music festival at 8:00 am. During the
first hour of ticket sales, 350 tickets sell. After the first hour, tickets sell at a rate of 75 tickets
per hour.
The average rate at which tickets sell, T(x), can be modeled by a rational function, where xis the
number of hours that the tickets have been on sale since 9:00 am.
Which of the following graphs correctly models the situation and gives the correct approximate
average rate of change of the average rate at which tickets sell over the hours of 10:00 am and
12:00 pm?
W.
X.
Y.
Z.
A. Z
C. Y
B. X
D. W
7. Timmy makes an initial deposit into an interest-bearing savings account, which is
compounded semi-annually at a fixed rate of 5.7%. After the initial deposit, Timmy does not
withdraw or deposit any money. The balance of the account can be modeled by the following
function, where x is the number of years since the initial deposit.
What does the y-intercept of A(x) represent?
A. the time it takes for the initial deposit to increase by 100%
B. the initial amount of money that Timmy deposits into the savings account
C. the amount of money that the bank pays to Timmy's account semi-annually
D. the rate at which the money in Timmy's account is increasing
8. Every summer, Richard plants a garden on a rectangular plot of land. Last summer, Richard's
garden measured 33 feet in length and 14 feet in width. This summer, Richard decides to resize
his garden by decreasing the length of the garden, and increasing the width of the garden by
two times the length reduction.
The area of this year's garden, A(x), can be modeled by a quadratic function, where x is the
number of feet that the length is reduced.
What is the maximum potential area of this year's resized garden?
A. 800 square feet
B. 26 square feet
C. 462 square feet
D. 1,600 square feet
9. Scott throws a ball in the air. After 6 seconds, he catches the ball. He knows that the ball
reaches a maximum height of 35 feet.
If the height of the ball, h(t), over time, t, can be modeled by a quadratic function, then which
of the following functions correctly models the situation above?
A.
B.
C. There is not enough information to determine
a model for the given situation.
D.
10. Every year, the price of a plane ticket from Kansas City to St. Louis is two-thirds of the price
of a plane ticket from Kansas City to Austin. The price of each ticket increases by 15% each year.
In the year 2000, a plane ticket from Kansas City to Austin cost $244.00.
Create a function, P(t), to model the price of a ticket from Kansas City to St. Louis t years after
the year 2000. Then, use the function to determine which of the following tables correctly
models the situation above and gives the correct average rate of change from 2001 to 2004.
A.
t
1
2
3
4
P(t)
$420.90
$484.03
$556.64
$640.14
Average Rate of Change: $73.08 per year
B.
t
1
2
3
4
P(t)
$280.60
$322.69
$371.09
$426.76
Average Rate of Change: $48.72 per year
C.
t
1
2
3
4
P(t)
$187.07
$215.13
$247.40
$284.51
Average Rate of Change: $32.48 per year
D.
t
1
2
3
4
P(t)
$117.53
$99.90
$84.91
$72.18
Average Rate of Change: $17.78 per year
11. Joe is playing horseshoes on his backyard horseshoe court. He built the court himself, and it
consists of a stake and a foul line, which is where players stand and pitch. Joe is standing at the
foul line, which is located 37 feet away from the stake, and he tosses a horseshoe.
The horseshoe's distance from the stake, d(x), can be modeled with an absolute value function,
where x is the distance the horseshoe has traveled.
Which of the following graphs correctly models the situation and gives the correct average rate
of change over the distances of 4 feet to 8 feet?
W.
X.
Y.
Z.
A. Z
C. X
B. W
D. Y
12. Andy made a spirometer for a physics experiment. The spirometer is designed to measure
the volume of air in a person's lungs. Andy found that when he breathes normally, he inhales
and exhales 0.5 of a liter of air per breath. He also found that when breathing normally, after
exhaling, he still has 2 liters of air in his lungs.
Andy recorded 15 breaths in one minute, starting at the beginning of an exhale.
If Andy inhaled and exhaled the exact same amount of air in each breath, which of the following
functions best models the amount of air in Andy's lungs t seconds after he started recording?
A.
B.
C.
D.
13. Throughout the day, the water level, h(t), at Sunny Beach varies with the tides. Joe, a
frequent visitor of Sunny Beach, arrived at the beach at 12:00 p.m., and collected the following
data, where t represents the number of hours since Joe arrived at the beach.
t
0
1
2
3
4
5
h(t)
5
4.41
3
1.59
1
1.59
Joe lost some of his data, but he knows that the highest tide occurs at 12:00 p.m., and he was
able to use a trigonometric function to model the height of the tide at any time.
What is the period of the function that can be used to model the height of the tide?
A. 8 hours
B. More information is needed to solve this problem.
C. 5 hours
D. 12 hours
14. Brad has a liter of water with a 2% concentration of salt. He also has an unlimited supply of
ocean water which contains a concentration of 3.5% salt.
As Brad adds ocean water to the original liter, the salt concentration, C(x), can be modeled by a
rational function, where x is the number of liters of ocean water added to the original liter.
Which of the following best describes the concentration of the mixture as Brad adds ocean
water to it?
A. There is not enough information to determine the salt concentration of Brad's
mixture.
B. The concentration of the mixture will always be greater than 3.5% salt.
C. The concentration of the mixture will always be less than 2% salt.
D. The concentration of the mixture will always be less than 3.5% salt.
15. The speed that a car is traveling prior to a collision, S(d), can be determined by evaluating
the square root of the product of the constant 25.5 feet per second squared and the distance
that the car skids, d, in feet. Which of the following correctly models the situation and gives the
rate of change over the skid distance of 10 feet to 14 feet?
A.
B.
C.
D.