Question

What is the function that reflects over the x-axis, vertically stretches by a factor of 3, shifts down 8 units, and shifts right 6 units?

Answer 1

The transformed function that reflects over the x-axis, stretches vertically by a factor of 3, shifts down 8 units, and right 6 units is represented as g(x) = -3f(x - 6) - 8.

Step-by-step explanation:

The function that reflects over the x-axis, vertically stretches by a factor of 3, shifts down 8 units, and shifts right 6 units can be represented as follows:

If the original function is f(x), then after the transformation, the new function g(x) will be:

g(x) = -3f(x - 6) - 8

This is because:

• Reflection over the x-axis is achieved by multiplying the function by -1.
• Vertical stretch by a factor of 3 is done by multiplying the function by 3.
• Shift down by 8 units is represented by subtracting 8 from the function.
• Shift right by 6 units is handled by replacing x with (x - 6).