Question

What transformation change occurs from q(x)=−3√x - 9 +4
to r(x)=-3√x - 2 + 4
?(1 point)
Responses

horizontal shift left 7 units
horizontal shift left 7 units

vertical shift right 7 units
vertical shift right 7 units

horizontal shift right 6 units
horizontal shift right 6 units

horizontal shift right 7 units

Answer 1

To analyze the transformation from \( q(x) = -3\sqrt{x - 9} + 4 \) to \( r(x) = -3\sqrt{x - 2} + 4 \), we first need to observe the arguments of the square root functions in both functions.

In \( q(x) \), the term under the square root is \( x - 9 \), indicating a horizontal shift to the right by 9 units. In the function \( r(x) \), the term under the square root is \( x - 2 \), indicating a horizontal shift to the right by 2 units.

To find the total horizontal shift from \( q(x) \) to \( r(x) \):

- The transformation from \( q \) to \( r \) involves moving from \( x - 9 \) to \( x - 2 \).
- This is a horizontal shift to the right from \( x = 9 \) to \( x = 2 \) (which you can also think of as moving the "starting point" closer from \( 9 \) to \( 2 \)).

To calculate the distance or difference:
\[
9 - 2 = 7
\]

Therefore, the transformation is a horizontal shift to the left by 7 units.

The correct response is: **horizontal shift left 7 units**.