Question

Which of the following statements describes the transformation indicated by:
f(x)=x^2
g(x)=(x-3)
(1 point)
Responses

Function f was translated (shifted) horizontally 3 units to the left.
Function f was translated (shifted) horizontally 3 units to the left.

Function f was translated (shifted) vertically 3 units down.
Function f was translated (shifted) vertically 3 units down.

Function f was translated (shifted) horizontally 3 units to the right.
Function f was translated (shifted) horizontally 3 units to the right.

Function f was translated (shifted) vertically 3 up. -6

Answer 1

To determine the transformation described by the functions \( f(x) = x^2 \) and \( g(x) = (x-3) \), we need to analyze how \( g(x) \) modifies \( f(x) \).

The function \( f(x) = x^2 \) represents a standard parabola that opens upwards. The function \( g(x) = (x - 3) \) indicates a horizontal shift.

In general, when you see a transformation like \( f(x - h) \), it involves shifting the graph of \( f(x) \) horizontally:
- If \( h > 0 \), the graph shifts to the right.
- If \( h < 0 \), the graph shifts to the left.

In this case, \( g(x) = (x - 3) \) suggests that the transformation performed is \( f(x - 3) \), which means the function \( f(x) \) is shifted **3 units to the right**.

Thus, the correct statement that describes the transformation is:

**Function \( f \) was translated (shifted) horizontally 3 units to the right.**