Question

Write an equation that represents f(x)=9 x after a reflection on the x-axis, a horizontal translation of 3 units left, and 5 units down.

Answer 1

The equation that represents f(x)=9x after a reflection on the x-axis, a horizontal translation of 3 units left, and 5 units down is y = -9(x-3) - 5.

Step-by-step explanation:

The equation that represents the transformation of f(x)=9x after a reflection on the x-axis, a horizontal translation of 3 units left, and 5 units down can be obtained by applying the transformations to the original equation:

1. A reflection on the x-axis changes the sign of the y-term, so we now have -9x.
2. A horizontal translation of 3 units left means subtracting 3 from the x-term, giving us -9(x-3).
3. A vertical translation of 5 units down means subtracting 5 from the y-term, resulting in -9(x-3) - 5.

Therefore, the equation that represents the transformed function is y = -9(x-3) - 5.