Math 30-1 Written Response Polynomials, Rationals, Functions
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School
Millwoods Christian School *
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Course
30
Subject
Mathematics
Date
Nov 24, 2024
Type
docx
Pages
9
Uploaded by CorporalThunder8499
Written-response Question 2
Use the following information to answer written-response question 2.
A particular polynomial function is given by . One factor of the polynomial function is .
Written Response-5 marks
●
Explain how to determine the value of k
, and then algebraically solve for k
. [2 marks]
Use the following information to answer the next part of written-response question 2.
A gift box has dimensions as shown in the diagram below.
●
Write an equation in factored form that represents the volume, V
, of the box as a function of x
. Algebraically determine the value of x
that would produce a volume of 24 units
3
. Determine the corresponding dimensions of the box. [3 marks]
Written-response Question 4
Use the following information to answer written-response question 4.
A rational function, , has the following features:
●
Horizontal asymptote at ●
y
-intercept at ●
Point of discontinuity at ●
Vertical asymptote at Written Response-5 marks
●
Determine the equation of . [2 marks]
Use the following information to answer the next part of written-response question 4.
The rational function is stretched vertically about the x
-axis by a factor of 5, and stretched horizontally about the y
-axis by a factor of . ●
Determine the equation of the transformed function and its corresponding domain and range. [3 marks]
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Written-response Question 5
Use the following information to answer written-response question 5.
The polynomial function , has a factor of .
Written Response-5 marks
●
Algebraically determine
the exact values of all zeros of the function. [2 marks]
●
If R
(
x
) is the result of translating P
(
x
) 1 unit to the left and 12 units up, then determine the equation of R
(
x
) and express it in the form and verify that x
– 3 is a factor of R
(
x
). [3 marks]
Written-response Question 7
Use the following information to answer written-response question 7.
The volume of a rectangular prism is and the length is Written Response-5 marks
●
Determine the width and the height of the rectangular prism. [3 marks]
●
The volume function is reflected about the x
-axis. Determine the resulting function and its contextual domain. [2 marks]
h
w
Written-response Question 8
Use the following information to answer written-response question 8.
The graph of the rational function is shown below. The equation of this graph can be written in the form with a vertical asymptote at , a horizontal asymptote at and a point of discontinuity at .
Written Response-5 marks
●
Determine the equation of the rational function in the form
. [3 marks]
●
The graph of is transformed into
. Sketch and state its
domain and range. [2 marks]
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Written-response Question 9
Use the following information to answer written-response question 9.
The function is given below.
Written Response-5 marks
●
Sketch the graph of the function and determine the following characteristics: domain, x
- and y
-intercepts, and the equation of the vertical asymptote(s) [2 marks]
●
If describe the transformations of and determine for the domain, x
- and y
-intercepts and the equation of the vertical asymptotes
[3 marks]
Written-response Question 16
Use the following information to answer written-response question 16.
A store is offering a one day discount of 10% off of all cell phones. They also offer warranty for their phones of either 5% of the discounted price or $35.
Written Response-5 marks
●
Model each warranty scenario as a function of the original price. [3 marks]
●
If the original price is $800, which warranty scenario is the better price and what is the price of each? Justify
your answer. [2 marks]
Written-response Question 17
Written Response-5 marks
●
The polynomial can be expressed in factored form of . Algebraically factor the polynomial function . [3 marks]
Use the following information to answer the next part of written-response question 17.
The polynomial functions and are graphed on a Cartesian plane.
●
Compare the x
-intercepts, y
-intercepts, and end behaviors of the polynomial functions. [2 marks]
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