1. graph

hi,

i'm currently doing questions on graphs of cubic functions and i'm encountering something i don't quite understand, the book keeps saying something like "the coefficient of $\displaystyle x^3$ is $\displaystyle + 2$ so the shape of the graph is the same as $\displaystyle y = x^3$ when x is numerically very large."

what does this mean and why? and why would it not be the case if x were small?

thanks for any info, mark

2. Originally Posted by mark
hi,

i'm currently doing questions on graphs of cubic functions and i'm encountering something i don't quite understand, the book keeps saying something like "the coefficient of $\displaystyle x^3$ is $\displaystyle + 2$ so the shape of the graph is the same as $\displaystyle y = x^3$ when x is numerically very large."

what does this mean and why? and why would it not be the case if x were small?

thanks for any info, mark
look at the graphs ...

$\displaystyle y = x^3$

$\displaystyle \textcolor{green}{y = 2x^3}$

$\displaystyle \textcolor{red}{y = \frac{1}{2}x^3}$

3. i see, so the larger the coefficient of x, the closer the line of the graph is to the y axis. but i thought it was more to do with what the actual value of $\displaystyle x^3$ was rather than the coefficient?