Consider the function
Which of the following statements is correct?
- The function
is continuous. - The graph of
has a vertical asymptote. - The graph of
has a horizontal asymptote. - The graph of
has a point of discontinuity.
Calculus, SPEC2 2022 VCAA 1
Consider the family of functions
- Write down the equations of the two asymptotes of the graph of
when . (2 marks)
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- Sketch the graph of
for on the set of axes below. Clearly label any turning points with their coordinates and label any asymptotes with their equations. (3 marks)
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- i. Find, in terms of
, the equations of the asymptotes of the graph of . (1 mark)
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- ii. Find the distance between the two turning points of the graph of
in terms of . (2 marks)
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- Now consider the functions
and , where and . - The region bounded by the curves of
and is rotated about the -axis.
-
- Write down the definite integral that can be used to find the volume of the resulting solid. (2 marks)
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- Hence, find the volume of this solid. Give your answer correct to two decimal places. (1 mark)
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- Write down the definite integral that can be used to find the volume of the resulting solid. (2 marks)
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a.
b.
c.i.
c.ii.
d.i.
d.ii.
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a.
b.
c.i.
c.ii.
d.i
d.ii.
♦♦ Mean mark (d)(ii) 37%.
Graphs, SPEC2 2022 VCAA 3 MC
The graph of
- two vertical asymptotes and one horizontal asymptote.
- two horizontal asymptotes and one vertical asymptote.
- a vertical asymptote with equation
and one horizontal asymptote with equation . - one horizontal asymptote with equation
and only one vertical asymptote with equation . - a horizontal asymptote with equation
and at least one vertical asymptote.
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♦♦ Mean mark 38%.
41% of students chose
41% of students chose
Functions, SPEC2 2023 VCAA 2 MC
The graph of
Functions, SPEC1 2023 VCAA 1
Consider the function
- Show that the rule for the function
can be written as . (1 mark)
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- Sketch the graph of
on the axes below, labelling any asymptotes with their equations. (3 marks)
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| a. | ||
b.
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| a. | ||
b.
Graphs, SPEC2-NHT 2019 VCAA 1 MC
The graph of which one of the following relations does not have a vertical asymptote?
Graphs, SPEC2 2019 VCAA 2 MC
The asymptote(s) of the graph of
Graphs, SPEC2 2011 VCAA 1 MC
The number of straight line asymptotes of the graph of
A. 0
B. 1
C. 2
D. 3
E. 4
Graphs, SPEC2 2012 VCAA 3 MC
The graph of
All the axes below have the same scale as the axes in the diagram above.
The graph of
| A. |  |
B. |  |
| C. |  |
D. |  |
| E. |  |
Graphs, SPEC2 2012 VCAA 1 MC
The graph with equation
A.
B.
C.
D.
E.
Algebra, SPEC2 2013 VCAA 3 MC
The graph of
Given that the graph has one stationary point with a
A.
B.
C.
D.
E.
Graphs, SPEC2 2016 VCAA 3 MC
The straight-line asymptote(s) of the graph of the function with rule
A.
B.
C.
D.
E.
Graphs, SPEC2-NHT 2017 VCAA 1 MC
The number of asymptotes of the graph of the function with rule
A. 0
B. 1
C. 2
D. 3
E. 4
Graphs, SPEC2 2014 VCAA 3 MC
The features of the graph of the function with rule
A. asymptotes at
B. asymptotes at
C. an asymptote at
D. an asymptote at
E. an asymptote at
Graphs, SPEC1 2018 VCAA 5
Sketch the graph of
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