Let
On the axes below, sketch the graph of
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Functions, 2ADV F2 2024 MET1 3*
Functions, 2ADV F2 EQ-Bank 2
A graph of the hyperbola
Find the values of
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Functions, 2ADV F2 2022 SPEC2 3 MC
The graph of
- two vertical asymptotes and one horizontal 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.
Functions, 2ADV F2 2023 MET1 3
- Sketch the graph of
on the axes below, labelling all asymptotes with their equation and axial intercepts with their coordinates. (3 marks)
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- Find the values of
for which . (1 mark) --- 2 WORK AREA LINES (style=lined) ---
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a.
b.
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a.
b.
♦♦ Mean mark (b) 38%.
MARKER’S COMMENT: Many students did not use their graph from part (a).
MARKER’S COMMENT: Many students did not use their graph from part (a).
Functions, 2ADV F2 SM-Bank 9 MC
The graph of the function
Functions, 2ADV F2 SM-Bank 20
- Sketch the graph of
on the axes below. Label asymptotes with their equations and axis intercepts with their coordinates. (3 marks)
- Find the values of
for which . (1 mark)
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a.
b.
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a.
b.
Functions, 2ADV F2 2021 HSC 19
Without using calculus, sketch the graph of
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Functions, 2ADV F2 EQ-Bank 9
Consider the function
- Find the domain of
. (1 mark)
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- Sketch
, showing all asymptotes and intercepts? (2 marks)
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| i. | ||
ii.
Functions, 2ADV F2 SM-Bank 12
Sketch the graph of
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COMMENT: Manipulation of the equation makes graphing much easier.
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Functions, 2ADV F2 EQ-Bank 11
On the axes below, sketch the graph of
Label all axis intercepts. Label each asymptote with its equation. (4 marks)
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Functions, 2ADV F2 SM-Bank 10
Consider the function
- Identify the domain of
. (1 mark)
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- Sketch the graph
, showing all intercepts and asymptotes. (3 marks)
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i.
ii.
COMMENT: Note that
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Functions, 2ADV’ F2 2007 HSC 3b
- Find the vertical and horizontal asymptotes of the hyperbola
and hence sketch the graph of . (3 marks)
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- Hence, or otherwise, find the values of
for which . (2 marks)
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i.
ii.
Functions, 2ADV’ F2 2012 HSC 13b
- Find the horizontal asymptote of the graph
. (1 mark)
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- Without the use of calculus, sketch the graph
, showing the asymptote found in part (i). (2 marks)
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| i. | ||
| ii. |
