# Graph Help

• Jun 12th 2007, 05:38 PM
wvmcanelly@cableone.net
Graph Help
I'm struggling with graphs. Any help appreciated. Thanks

The figure shows the graphs of
f(x) = x3 and g(x) = ax3. What can
you conclude about the value of
a?

a.
a < –1
b . –1 <
a < 0
c . 0 <
a < 1

d . 1 <
a

• Jun 12th 2007, 07:08 PM
ThePerfectHacker
We see the following:

1)\$\displaystyle f(x) = g(x) \mbox{ for }x=0\$
2)\$\displaystyle f(x) > g(x) \mbox{ for }x>0\$
3)\$\displaystyle f(x) < g(x) \mbox{ for }x<0\$

Let us examine #2:

We know that \$\displaystyle f(x) = x^3 \mbox{ and }g(x)=ax^3\$
Thus,
\$\displaystyle x^3 > ax^3 \mbox{ for }x>0\$
\$\displaystyle x^3 - ax^3>0\$
\$\displaystyle x^3 (1 - a) > 0\$
Since \$\displaystyle x>0 \Rightarrow x^3 >0\$
Thus, \$\displaystyle (1-a)>0 \Rightarrow a<1\$.

Let us examine #3:
We know that \$\displaystyle x^3 < ax^3 \mbox{ for } x<0\$
\$\displaystyle x^3 - ax^3 < 0\$
\$\displaystyle x^3 ( 1 - a) < 0\$
This leads to, \$\displaystyle a<1\$ but we already know that, so we did not gain anything.

But if we look at \$\displaystyle g(x)\$ we see that \$\displaystyle g(x)>0\$ for \$\displaystyle x>0\$.
Thus,
\$\displaystyle ax^3 \mbox{ for }x>0\$
Since \$\displaystyle x>0\$ it tells us that \$\displaystyle a>0\$.

Thus,
\$\displaystyle 0<a<1\$.
• Jun 12th 2007, 07:09 PM
wvmcanelly@cableone.net
Thanks, And I appreciate the tip about the format to use for pic.
• Jun 12th 2007, 07:11 PM
ThePerfectHacker
Quote:

Originally Posted by wvmcanelly@cableone.net
Thanks, And I appreciate the tip about the format to use for pic.

Just do not make your picture TOO BIG because then I have to scroll all the way to the right. And I cannot make the resolution smaller because my eyesight is that of Jules Henri Poincare.
• Jun 12th 2007, 07:13 PM
wvmcanelly@cableone.net
Note taken,
Thanks