Midterm 1 Practice Exam Solutions - Math 32, University Of California, Berkeley, Fall 2012 Page 3
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4MATH 32 FALL 2012
MIDTERM 1 - PRACTICE EXAM SOLUTIONS
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(a) What is the largest interval on which
is increasing?
Solution: [ 2 1].
(b) Let
be the function defined by restricting the domain of
to the interval from (a).
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Estimate the value of
(0).
Solution: There are two -values (inputs of
) corresponding to the -value (output
of
) 0 on the graph of
, which I approximate to be
1 and
3.
3 is not in the
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restricted interval [ 2 1], but
1 is. So
(0)
1.
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(c) Sketch a graph of
( ).
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Solution: (
in black, the reflection line
=
in grey,
in blue)
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(5) Let ( ) = 3
2 + 1.
(a) The graph of
is a parabola. Find the coordinates of the vertex of this parabola.
Solution: We’ll complete the square.
2
1
2
( ) = 3
+
3
3
2
1
1
1
= 3
+
3
9
3
2
1
2
= 3
+
3
9
2
1
2
= 3
+
3
3
1
2
The quadratic is now in vertex form, and we see that the vertex is
.
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