Question

Modify the equation of the function f(x)=log₂ x to reflect it upsidedown, translate 3 left, and translate down 7.

Answer 1

To modify the equation f(x) = log₂ x to reflect it upside down, translate 3 left, and translate down 7, follow these steps: take the negative of the original equation, reflect the equation upside down, translate 3 units left, and translate down 7.

Step-by-step explanation:

To modify the equation f(x) = log₂ x to reflect it upside down, translate 3 left, and translate down 7, you can follow these steps:

1. Take the negative of the original equation by multiplying f(x) by -1.
2. Reflect the equation upside down by taking the reciprocal of the value inside the logarithm. The equation becomes f(x) = -1/log₂ x.
3. To translate 3 units left, subtract 3 from x. The equation becomes f(x) = -1/log₂(x - 3).
4. To translate down 7 units, subtract 7 from the entire equation. The final equation is f(x) = -1/log₂(x - 3) - 7.