Answer
$f(x)=-2x^3$
Work Step by Step
Since the graph follows the shape $f(x)=x^3$ we will start with that equation:
$f(x)=x^3$
First notice the function is reflected across the y-axis. To reflect across the y-axis substitute -x for x in the right side of the equation:
$f(x)=(-x)^3=-x^3$
Second, notice the graph has been stretched vertically (by a factor of k) and will follow the below equation:
$f(x)=-kx^3$
Substitute (1,-2) into the above equation to solve for k:
$-2=-k(1)^3$
$k=2$
So we get the final function:
$f(x)=-2x^3$
