Thread: sketching curves-transformation curves f(x)!!!!

Hi, not sure what to do here. please help.

find the equations of the curves y=f(x+2) and y=f(x)+2, in terms of x, and use these equations to find the coordinates of the points where these curves cross the y-axis.

Originally Posted by becca999

Hi, not sure what to do here. please help.

find the equations of the curves y=f(x+2) and y=f(x)+2, in terms of x, and use these equations to find the coordinates of the points where these curves cross the y-axis.

It looks like you have not given us enough information here. I think we will
need to know something about f.

RonL

well it a says y=f(x) where f(x)=(x-1)(x+2) but then how do you work out the equations of the curves y=f(x+2) and y=f(x)+2 in therms of x and finding coordinates??

Originally Posted by becca999

well it a says y=f(x) where f(x)=(x-1)(x+2) but then how do you work out the equations of the curves y=f(x+2) and y=f(x)+2 in therms of x and finding coordinates??

If $\displaystyle f(x)=(x-1)(x+2)$, then

$\displaystyle
f(x+2)=((x+2)-1)((x+2)+2)=(x+1)(x+4)
$

so the equation of $\displaystyle y=f(x+2)$ is:

$\displaystyle y=(x+1)(x+4)$

similarly:

$\displaystyle y=f(x)+2=(x-1)(x+2)+2=x^2+x=x(x+1)$

so:

$\displaystyle y=x(x+1)$

RonL