Question

Use transformations of the absolute value function, f(x)= |x|, to graph the function g(x)= -|x-1| +2

Answer 1

Explanation

From the statement, we know that the original function is f(x) = |x|, and the transformed function:

$g(x)=-|x-1|+2.$

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