Question

Given the parent function f(x) = 2x + 4, select the two transformations used to get the new function g(x) = -2x + 1.

A) Reflection in the x-axis and horizontal stretch by a factor of 2
B) Vertical stretch by a factor of 2 and vertical shift down by 3 units
C) Vertical stretch by a factor of 2 and horizontal shift to the right by 3 units
D) Horizontal shift to the left by 3 units and vertical shift up by 1 unit

Answer 1

The two transformations used to get the new function g(x) = -2x + 1 from the parent function f(x) = 2x + 4 are a reflection in the x-axis and a vertical shift down by 3 units.

Step-by-step explanation:

The two transformations used to get the new function g(x) = -2x + 1 from the parent function f(x) = 2x + 4 are:

1. Reflection in the x-axis, which changes the sign of the y-values. This is represented by the negative sign in front of the 2 in -2x.
2. Vertical shift down by 3 units, which changes the y-intercept. This is represented by the constant term +1 in the equation.

Therefore, the correct answer is B) Vertical stretch by a factor of 2 and vertical shift down by 3 units.