Question

Given f(x) is a function, check all transformations that were applied to f(x) to get g(x)=f(−1(x−5))+7

A. Shifts Left
B. Shifts Right
C. Vertical Reflection
D. Vertical Stretch
E. Shifts Down
F. Horizontal Reflection
G. Shifts Up
H. Vertical Shrink

Answer 1

The function g(x) = f(−1(x−5)) + 7 underwent a horizontal reflection, a shift 5 units to the right, and a vertical shift 7 units up, represented by the transformations F, B, and G respectively.

Step-by-step explanation:

To determine the transformations applied to the function f(x) to get g(x) = f(−1(x−5)) + 7, let's analyze each part of g(x) step by step:

1. A horizontal reflection is noted by the negative sign inside the function, which flips the graph over the y-axis, so f(−x) would be a horizontal reflection. Because the negative is multiplied by 1, it doesn't affect the stretch or shrink.
2. The (x−5) inside of the function indicates a horizontal shift. Since we're subtracting 5 from x, the function shifts 5 units to the right, not the left.
3. The + 7 outside of the function indicates a vertical shift. Because we are adding 7 to the function, it moves 7 units up.

Therefore, the transformations applied to f(x) to get g(x) are:

• Horizontal Reflection (F)
• Shifts Right (B)
• Shifts Up (G)