Question

Identify each function as a translation, compression, stretch, or reflection of the parent function, f(x)=x^2.

(The second function is in the picture.)
A. g(x)=-x^2
C. f(x)=(x+3)^2

Answer 1

The function g(x) = -x^2 is a reflection of the parent function f(x) = x^2 across the x-axis, and the function f(x) = (x+3)^2 is a translation of the parent function 3 units to the left.

Step-by-step explanation:

The student is working with transformations of the parent function f(x) = x^2, which is a quadratic function. For the function g(x) = -x^2, this represents a reflection of the parent function across the x-axis, because the negative sign in front of the x^2 inverts all the y-values of the parent function. For the function f(x) = (x+3)^2, this is a translation of the parent function 3 units to the left, as indicated by the addition of 3 inside the parentheses.