Question

Write the equation for an absolute value function that is translated 7 units down and vertically compressed by a factor of 0.75.

A) y = 0.75| x - 7 |
B) y = -0.75| x + 7 |
C) y = 0.75| x + 7 |
D) y = -0.75| x - 7 |

Answer 1

The equation for the given absolute value function is y = -0.75| x - 7 |.

Step-by-step explanation:

The equation for an absolute value function that is translated 7 units down and vertically compressed by a factor of 0.75 is y = -0.75| x - 7 | (option D).

To understand this, let's break it down:

1. The negative sign in front of the absolute value indicates that the function is reflected vertically.
2. The factor of 0.75 in front of the absolute value compresses the graph vertically.
3. The (x - 7) inside the absolute value indicates a translation to the right by 7 units.

Therefore, the correct equation that satisfies all the given conditions is y = -0.75| x - 7 |.