## Algebra and Trigonometry 10th Edition

$f(x)=-2x^3$
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: $f(x)=-2x^3$