Name: _____________________
Class: _________________
AU10: Notes & HW – Lesson 9
Date: _________________
1. Students and adults purchased tickets for a recent basketball playoff game. All tickets were
sold at the ticket booth—season passes, discounts, etc. were not allowed. (M1:EM#7 – AU4)
Student tickets cost $5 each, and adult tickets cost $10 each.
A total of $4500 was collected. 700 tickets were sold.
a) Write a system of equations that can be used to find the number of student tickets, s, and
the number of adult tickets, a, that were sold at the playoff game.
b) Assuming that the number of students and adults attending would not change, how much
more money could have been collected at the playoff game if the ticket booth charged
students and adults the same price of $10 per ticket?
c) Assuming that the number of students and adults attending would not change, how much
more money could have been collected at the playoff game if the student price was kept at $5
per ticket and adults were charged $15 per ticket instead of $10?
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2. Weather data were recorded for a sample of 25 American cities in one year. Variables
measured included January high temperature (in degrees Fahrenheit), January low
temperature, annual precipitation (in inches), and annual snow accumulation. The
relationships for three pairs of variables are shown in the graphs below (Jan Low
Temperature – Graph A; Precipitation – Graph B; Annual Snow Accumulation – Graph C).
a. Which pair of variables will have a correlation coefficient closest to 0? (M2:EM#4 – AU5)
A. Jan high temperature and Jan low temperature
B. Jan high temperature and Precipitation
C. Jan high temperature and Snow accumulation
Explain your choice:
b. Which of the above scatterplots would be best described as a strong nonlinear relationship?
Explain your choice:
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3. Given hx   x  2  3 and g x    x  4 .
a. Describe how to obtain the graph of g from the graph of ax   x using transformations.
b. Describe how to obtain the graph of h from the graph of ax   x using transformations.
c. Sketch the graphs of hx  and g x on the same coordinate plane. (M3:EM#1 – AU2/4)
y
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
–2
–3
–4
–5
–6
–7
–8
d. Use your graphs to estimate the solutions to the equation:
x  2 3  x  4
Explain how you got your answer.
e. Were your estimations you made in part (d) correct? If yes, explain how you know. If not
explain why not.
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4. A boy bought 6 guppies at the beginning of the month. One month later the number of
guppies in his tank had doubled. His guppy population continued to grow in this same manner.
His sister bought some tetras at the same time. The table below shows the number of tetras, t,
after n months have passed since they bought the fish. (M3:EM#3 – AU3/6*)
a. Create a function g to model the growth of the boy’s guppy population, where g(n) is the
number of guppies at the beginning of each month, and n is the number of months that have
passed since he bought the 6 guppies. What is a reasonable domain for g in this situation?
b. How many guppies will there be one year after he bought the 6 guppies?
c. Create an equation that could be solved to determine how many months after he bought the
guppies there will be 100 guppies.
d. Use graphs or tables to approximate a solution to the equation from part (c). Explain how you
arrived at your estimate.
y
x
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e. Create a function, t, to model the growth of the sister’s tetra population, where t(n) is the
number of tetras after n months have passed since she bought the tetras.
f. Compare the growth of the sister’s tetra population to the growth of the guppy population.
Include a comparison of the average rate of change for the functions that model each
population’s growth over time.
g. Use graphs to estimate the number of months that will have passed when the population of
guppies and tetras will be the same.
y
x
h. Use graphs or tables to explain why the guppy population will eventually exceed the tetra
population even though there were more tetras to start with.
i. Write the function g(n) in such a way that the percent increase in the number of fish per month
can be identified. Circle or underline the expression representing percent increase in number of
fish per month.
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5. The graph of a piecewise function f is shown to the right. The domain of f is  3  x  3 .
a. Create an algebraic representation for f. Assume that the graph of f is composed of straight line
segments. (M3:EM#5 – AU2)
b. Sketch the graph of y  2 f x  and state the domain and range.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
–2
–3
–4
–5
–6
c. How does the range of y  f x  compare to the range of y  kf x , where k  1 ?
6
2
3
4
5
6
x
d. Sketch the graph of y  f 2 x  and state the domain and range.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
–2
–3
–4
–5
–6
e. How does the domain of y  f x  compare to the domain of y  f kx , where k  1 ?
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4
5
6
x
6. An arrow is shot into the air. A function representing the relationship between the number of
seconds it is in the air, t, and the height of the arrow in meters, h, is given by:
(M4:EM#3 – AU9*)
ht   4.9t 2  29.4t  2.5
a. Complete the square for this function.
b. What is the maximum height of the arrow? Explain how you know.
c. How long does it take the arrow to reach its maximum height? Explain how you know.
d. What is the average rate of change for the interval from t = 1 to t = 2 seconds? Compare your
answer to the average rate of change for the interval from t = 2 to t = 3 seconds and explain the
difference in the context of the problem.
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e. How long does it take the arrow to hit the ground? Show your work or explain your answer.
f. What does the constant term in the original equation tell you about the arrow’s flight?
g. What do the coefficients on the second- and first-degree terms in the original equation tell you
about the arrow’s flight?
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(M4:EM#4 – AU7)
7. Rewrite each expression below in expanded (standard) form:

a. x  3


2

b. x  2 5 x  3 5

c. Explain why, in these two examples, the coefficients of the linear terms are irrational and why
the constants are rational.
Factor each expression below by treating it as the difference of squares:
e. t  16
d. q 2  8
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8. Solve the following equations for r. Show your method and work.
If no solution is possible, explain how you know.
(M4:EM#5 – AU7)
a. r 2  12r  18  7
c. r 2  18r  73  9
b. r 2  2r  3  4
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