Question

The parent function f(x)=x^2 is reflected across the x-axis, vertically stretched by a factor of 4, and translated right 10 units to create g(x). Use the description to write g(x).

A. g(x)=-4(x-10)^2
B. g(x)=4(-x-10)^2
C. g(x)=-(4(x-10))^2
D. g(x)=4(-(x-10))^2

Answer 1

The function g(x) that results from reflecting f(x), stretching it vertically by a factor of 4, and translating it right by 10 units is g(x) = -4(x - 10)^2.

Step-by-step explanation:

The student's question involves transforming the parent function f(x) = x^2. We're given a series of transformations, which include a reflection across the x-axis, a vertical stretch by a factor of 4, and a horizontal translation to the right by 10 units. To apply these transformations to the function, first, the reflection across the x-axis will multiply the function by -1, resulting in -f(x).

A vertical stretch by a factor of 4 is achieved by multiplying the function by 4, resulting in 4(-f(x)). Lastly, a horizontal shift to the right by 10 units is represented by replacing x with (x - 10). Putting all these transformations together, we obtain g(x) = -4(x - 10)^2, which corresponds to option A.