Question

What transformations are applied to the function f(x) = -3(x - 4)² + 3?

a. Vertical stretch, reflection, horizontal translation right 4, vertical translation up 3
b. Horizontal stretch, reflection, vertical translation down 4, horizontal translation up 3
c. Vertical compression, no reflection, horizontal translation left 4, vertical translation down 3
d. No transformation, reflection, horizontal translation right 4, vertical translation up 3

Answer 1

The function f(x) = -3(x - 4)² + 3 undergoes a vertical stretch by a factor of 3, reflection across the x-axis, horizontal translation right 4 units, and vertical translation up 3 units.

Step-by-step explanation:

The given function f(x) = -3(x - 4)² + 3 can be analyzed by looking at the transformations applied to the parent function f(x) = x². In this case, the transformations are as follows:

• A reflection in the x-axis is seen by the negative sign in front of the 3, making it reflect across the x-axis.
• A vertical stretch by a factor of 3 is noted by the coefficient 3 in front of the parenthesis.
• A horizontal translation 4 units to the right is indicated by the (x - 4) portion of the function, showing a horizontal shift.
• Lastly, a vertical translation 3 units upwards is seen by the +3 outside of the squared term, representing a vertical shift.

Therefore, the correct transformation applied to the function is a vertical stretch by a factor of 3, a reflection across the x-axis, a horizontal translation 4 units to the right, and a vertical translation 3 units up. This corresponds to option a.