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MATH 180\hfill FALL 1995

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\centerline{ASSIGNMENT \#6}

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1.9, \#1.
Stretching the graph of $y=x^2$ vertically by a factor of
2 gives the graph of $y=2x^2$.  Shifting this last graph
upwards by one unit gives the graph of $y-1=2x^2$ or $y=2x^2+1$.
Now interchange the order of the stretch and shift operations.
Shifting the graph of $y=x^2$ upwards gives
the graph of $y-1=x^2$ or $y=x^2+1$.  Stretching this last graph
vertically by a
factor of 2 gives the graph of $y=2x^2+2$.  So interchanging
the operations gives a different graph.
Comment:  The incorrect answer $y=x^2+2$ was given for part (b) by a
number of students.  Compare this with the answer given above.

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1.9, \#2.  $g(f(x))=\log(2x+3)$,
$f(g(x))=(2\log x)+3$, $f(f(x))=2(2x+3)+3=4x+9$.

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1.10, \#20, 21.
The period of the earth's revolution around the sun is about a year
or 365 days.
The period of the moon's revolution around the earth is about
29 days.

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1.10, \#33, 35.
Possible functions are $y=2\sin (x/4)$ and $y=5\cos (x/3)$.
A common mistake:  Writing $4x$ and $3x$ instead of $x/4$ and
$x/3$.

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