1. ## 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

2. 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,
$\displaystyle 0<a<1$.

3. Thanks, And I appreciate the tip about the format to use for pic.

4. 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.

5. Note taken,
Thanks