Question

How does the function g(x) = 1/2*|x-4| transform the function f(x) = |x-4)?

A) g(x) stretches f(x) vertically by a factor of 2.
B) g(x) compresses f(x) horizontally by a factor of 2.
C) g(x) shifts f(x) horizontally 4 units to the right.
D) g(x) shifts f(x) vertically 1/2 unit up.

Answer 1

The function g(x) = 1/2*|x-4| stretches the function f(x) = |x-4| vertically by a factor of 2.

Step-by-step explanation:

The function g(x) = 1/2*|x-4| transforms the function f(x) = |x-4| in the following way:

1. The coefficient in front of the absolute value, 1/2, stretches the graph vertically by a factor of 2. This means that the y-values of g(x) will be half the size of the corresponding y-values of f(x).
2. The function is not compressed or stretched horizontally, so option B is incorrect.
3. The function is not shifted horizontally, so option C is also incorrect.
4. The function is not shifted vertically, so option D is also incorrect.

Therefore, the correct answer is A) g(x) stretches f(x) vertically by a factor of 2.