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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