Question

Which two transformations can be used to obtain the graph of g(x) = |-(x-7)| from the graph of f(x) = |x|?

A. A translation to the right 7 units followed by a reflection across the x-axis.
B. A translation to the left 7 units followed by a reflection across the x-axis.
C. A translation to the right 7 units followed by a reflection across the y-axis.
D. A translation to the left 7 units followed by a reflection across the y-axis.

Answer 1

To obtain the graph of g(x) = |-(x-7)| from the graph of f(x) = |x|, we need to apply a translation to the right 7 units followed by a reflection across the x-axis. Hence, A) is correct.

Step-by-step explanation:

To obtain the graph of g(x) = |-(x-7)| from the graph of f(x) = |x|, we need to apply two transformations. First, we need to translate the graph of f(x) 7 units to the right.

This can be done by replacing x with x - 7 in f(x). Second, we need to reflect the translated graph across the x-axis. This can be done by taking the opposite of the function, resulting in -g(x).

Therefore, the correct answer is A. A translation to the right 7 units followed by a reflection across the x-axis.