The function f(x)=x2 is transformed 3 times to become f(−x+4)+3 . Select the correct transformations below. (3 points) The function was translated 4 units (left/right) and 3 units (up/down) , and reflected over the (x/y) axis.

Answer 1

To analyze the transformation applied to the function \( f(x) = x^2 \) to become \( f(-x + 4) + 3 \), let's break it down step by step.

1. Starting Function: \( f(x) = x^2 \)

2. Inside the Function: \( f(-x + 4) \)

   • The \(-x\) indicates a reflection over the y-axis.
   • The \( +4 \) indicates a horizontal translation. Specifically, it shifts the graph to the left by 4 units (because you can think of this as translating the input by \( -4 \)).

3. Outside the Function: \( +3 \)

   • This indicates a vertical translation of 3 units up.

Combining these transformations:

• The function is reflected over the y-axis.
• Then, it is translated 4 units left.
• Finally, it is translated 3 units up.

Hence, the correct transformations for \( f(-x + 4) + 3 \) are:

• Reflected over the y-axis
• Translated 4 units left
• Translated 3 units up

So the correct answer is:

• The function was translated 4 units left, 3 units up, and reflected over the y-axis (not the x-axis).