Preliminary Mathematics
Functions and Graphs TEST
NSW Syllabus Ref: 4.1, 4.2
© Mathematics Plus, 2002
Q1.
If f(
x
) =
x
3
�
x
� 2, then f(�2) =
�12
�10
�8
�6
all
x
Q3.
If f(
x
) =
x
3
�
x
2
+ 2
x
+ 3 and g(
x
) = 2, then g(f(
x
)) =
�2
x
4
+ 2
x
3
� 4
x
� 6
2
�6
11
Q5.
If f(
x
) =
x
3
� 2
x
2
+
c
and f(1) = 2, what is the value of
c
?
�2
0
2
3
Q6.
Which of the following equations has a graph that is symmetric about the
y
�axis?
y
=
x
3
�
x
y
=
x
4
�
x
2
+ 1
y
=
x
3
+
x
+ 1
y
= (1 +
x
)
�1
Q7.
The function
y
=
x
3
+
x
+ 1 has exactly one real zero. It is between
2 and 3
1 and 2
�1 and 0
�2 and �1
Q8.
If the roots of f(
x
) = 0 are �1 and 2, then the roots of f(2
x
) = 0 are
1 and �2
�1 and 2
½ and �1
� ½ and 1
Q9.
Which of the following is a reflection of the graph
y
= f(
x
) in the
y
�axis?
y
= f(�
x
)
y
= � f(
x
)
y
= |f(
x
)|
y
= � f(
�x
)
Q10.
If f(
x
) = 4 �
x
2
and g(
x
) = 2
x
, then the range of
y
= g(f(
x
)) is
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