Question

What is the resulting transformation of the function F(x)=∣x−3∣+5 when it undergoes a reflection over the x-axis, followed by a translation 4 units to the left, and then a translation down 3 units?

Answer 1

The resulting transformation of the function F(x)=∣x−3∣+5 when it undergoes a reflection over the x-axis, followed by a translation 4 units to the left, and then a translation down 3 units is F(x-4)-3=-∣x−7∣-8.

Step-by-step explanation:

To find the resulting transformation of the function F(x)=∣x−3∣+5 when it undergoes a reflection over the x-axis, followed by a translation 4 units to the left, and then a translation down 3 units, we can break down the steps:

1. Reflection over the x-axis: This will change the sign of the function, so we have F(x)=-∣x−3∣-5.
2. Translation 4 units to the left: This is represented by F(x-4)=-∣x−7∣-5.
3. Translation down 3 units: This is represented by F(x-4)-3=-∣x−7∣-8.

Therefore, the resulting transformation is F(x-4)-3=-∣x−7∣-8.