Explanation
From the statement, we know that the original function is f(x) = |x|, and the transformed function:
[tex]g(x)=-|x-1|+2.[/tex]
We know that:
0. f(x) → g(x) = -f(x) constitues a reflection across the x-axis,
,
1. f(x) → g(x) = f(x - 1) with a > 0 constitues a horizontal shift in 1 unit to the right,
,
2. f(x) → g(x) = f(x) + 2 with constitues a vertical shift in 2 units up.
Comparing f(x) and g(x), and taking into account the facts above, we see that the transformations needed to transform f(x) to g(x) are:
0. E. Reflection about the x-axis,
,
1. D. Horizontal shift,
,
2. C. Vertical shift.
Answer
• C. Vertical shift
,
• D. Horizontal shift
,
• E. Reflection about the x-axis
