Question

Describe the transformations to f(x) that resulted in the new function g)x)
g(x)=-f(3x)+2

Answer 1

The transformations to f(x) resulting in the new function g(x) = -f(3x)+2 include a reflection across the x-axis, a horizontal compression by a factor of 1/3, and a vertical translation up by 2 units.

Step-by-step explanation:

The student is inquiring about the transformations applied to an original function f(x) that create a new function g(x) = -f(3x)+2. To describe these transformations, we first identify each change to f(x):

• The multiplication by -1 in front of the function reflects f(x) across the x-axis.
• The argument (3x) inside the function indicates a horizontal compression by a factor of 1/3.
• The addition of +2 after the function translates the graph of f(x) up by 2 units on the y-axis.

It's important to note that these transformations occur sequentially and affect the graph's shape and position in the coordinate plane. Given that at x = 3, f(x) is positive with a positive, decreasing slope, neither of the example functions (a) y = 13x nor (b) y = x² in the reference can be used to deduce the exact form of f(x).