Math-UA.009辅导 、讲解 Python/c++程序
Math-UA.009. Written Homework
MATH-UA-009 — Algebra, Trigonometry and Functions
Professor Charles Stine
Name: Homework Assignment #5
NetID: Due Date: October 14th, 2024, 11:59 PM
• This homework should be submitted via Gradescope by 23:59 on the date
listed above. You can ffnd instructions on how to submit to Gradescope on
our Campuswire channel.
• There are three main ways you might want to write up your work.
– Write on this pdf using a tablet
– Print this worksheet and write in the space provided
– Write your answers on paper, clearly numbering each question and part.
∗ If using either of the last two options, you can use an app such as
OfffceLens to take pictures of your work with your phone and convert
them into a single pdf ffle. Gradescope will only allow pdf ffles to be
uploaded.
• You must show all work. You may receive zero or reduced points for
insufffcient work. Your work must be neatly organised and written.
You may receive zero or reduced points for incoherent work.
• If you are writing your answers on anything other than this sheet, you should
only have one question per page. You can have parts a), b) and c) on the
page for example, but problems 1) and 2) should be on separate pages.
• When uploading to Gradescope, you must match each question to the
page that your answer appears on. If you do not you will be docked a
signiffcant portion of your score.
• When appropriate put a box or circle around your ffnal answer.
• The problems on this assignment will be graded on correctness and completeness.
•
These problems are designed to be done without a calculator. Whilst there is
nothing stopping you using a calculator when working through this assignment,
be aware of the fact that you are not permitted to use calculators on exams
so you might want to practice without one.
1Math-UA.009. Written Homework
1. Find the domain of each of the following functions. Make sure to show all your
work.
(a) (4 points) f(x) =
1
√
x
2 − 4x − 12
(b) (3 points) v (t) =
5
t − 3
+
√
t − 1 + 1
2. For the following functions, ffnd the average rate of change over the given
interval.
(a) (1 point) f(x) = 1 − x
2 over [1, 2]
(b) (1 point) f(x) = x
2 + 3x over [−1, 1]
(c) (1 point) f(x) = x
3 − 5x + 2 over [−2, −1]
(d) (1 point) f(x) =
x + 2
2x − 1
over [3, 8]
2Math-UA.009. Written Homework
3. (2 points) The height of an object dropped from the roof of a building is
modeled by the function h(t) = −16t
2 + 64, for 0 ≤ t ≤ 2. Here, h(t) is the
height of the object off the ground in feet t seconds after the object is dropped.
Find and interpret the average rate of change of h over the interval [0, 2].
4. The graph of f(x) is shown below
(a) (2 points) Find the domain and range of the function. Write your answers
in interval notation.
(b) (2 points) For what value(s) of x is f(x) = 9?
(c) (2 points) On what interval(s) is f increasing? On what interval(s) is f
decreasing?
3Math-UA.009. Written Homework
5. A local retailer selling PortaBoy gaming systems is trying to mathematically
model the relationship between the number of PortaBoy systems sold in a week
and the price per system. Assume that this relationship is linear. Suppose 21
systems were sold in a week when the price was $215 per system but when the
systems went on sale for $180 each, weekly sales doubled (that is, they went
up to 42 systems).
(a) (4 points) Find a formula for a linear function p which represents the
price p(x) as a function of the number of systems sold, x.
(b) (3 points) Find the x and y intercepts of the graph of p(x) and sketch
the graph of p(x).
(c) (1 point) If the retailer wants to sell 120 PortaBoys next week, what
should the price be?
(d) (2 points) How many systems would sell if the price per system were set
at $120?
4Math-UA.009. Written Homework
6. (7 points) Given the function h(x) =
2
x
2 + 1
complete the table of values
shown below and use it to sketch h(x). State the domain and range of h using
interval notation and justify your answer for the range.
x h(x)
−2
−1
0
1
2
5Math-UA.009. Written Homework
7. (5 points) Let f(x) = x
2 and g(x) = −(x + 2)2 + 1.
(a) (3 points) Write down the sequence of transformations that need to be
made in order to obtain the graph of g(x) from the graph of f(x). Remember
that order matters.
(b) (2 points) Sketch the graph of f(x) and the graph of g(x) on the same
set of axes, using your answer in part (a).
6