There is a math student in distress over Algebra 2. Pi-Guy quickly travels to go tutor the student. Here is Pi-Guy’s movement to travel to the student: he flips downward, flies 10 units to the right, and then down 3 units. Write the equation f(x) to show the movements that Pi-Guy makes from his original location shown below. You do not need the specific type of function, just write in terms of f(x).
f(x) = -x + 10 - 3
To write the equation f(x) to show Pi-Guy's movements, we can break down his movements into three steps:
1. Flipping downward: This movement does not change the x-coordinate but flips the y-coordinate. Therefore, we can represent it as f(x) = (x, -y).
2. Flying 10 units to the right: This movement only affects the x-coordinate, increasing it by 10 units. We can represent it as f(x) = (x + 10, -y).
3. Moving down 3 units: This movement only affects the y-coordinate, decreasing it by 3 units. We can represent it as f(x) = (x + 10, -y - 3).
Combining all these movements, we can write the equation f(x) = (x + 10, -y - 3) to represent the movements Pi-Guy makes from his original location.
To represent Pi-Guy's movements from his original location, we can use the equation f(x) = -x^2 + 10x - 3.
Here's how each part of the movement is represented in the equation:
- "flips downward" can be represented by -x^2, indicating a downward movement.
- "flies 10 units to the right" can be represented by 10x, indicating a movement to the right.
- "down 3 units" can be represented by -3, indicating a downward movement of 3 units.