HSC Mathematics Extension 2 TEST
Graphs
NSW Syllabus Ref: Topic 1
© Mathematics Plus, 2002
The line
x
= 2 is a vertical asymptote.
The line
x
= 1 is a vertical asymptote.
The graph has no vertical or horizontal asymptotes.
The line
x
= �1/4 is a horizontal asymptote.
Q2.
The tangent to the curve
y
2
�
xy
+ 4 = 0 is vertical when
x
= 0
y
= 1/2
Q3.
The equation of the tangent to the hyperbola
x
2
�
y
2
= 3 at the point (2, 1) is
y
= 2
x
y
�
x
+ 3 = 0
y
� 2
x
+ 3 = 0
y
� 2
x
= 3
Q4.
The graph of
y
2
=
x
2
� 2
x
+ 5 is symmetric about
the
x
� axis
the
y
� axis
the origin
the
x
� and
y
� axes
Q5.
What might be the equation of the graph drawn below?
Q6.
Which of following statements referring to the graph of
y
2
=
x
3
�
x
is
not
true?
The graph is symmetric about the
x
� axis.
The line
x
= 1 is a vertical tangent.
The graph has no vertical or horizontal asymptotes.
Q7.
If the graph of
y
=
x
3
+
x
+
c
has exactly one
x
� intercept then
c
must be positive
c
must be negative
c
must equal zero
c
can be any value
Q8.
What might be the equation of the graph drawn below?
Q9.
The graph of
y
=
e
x
/2 is reflected in the line
y = x
. The equation of the reflected graph is
y
=
2 ln
x
e
�x
/2
½ ln
x
e
2
x
Q10.
If the graph of
y
=
x
3
�
x
+
c
has exactly two
x
� intercepts then
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