Question

Describe the transformations of the function g(x) from the parent function, f(x) = |x|.

g(x) = −|x−5|+2


A) The graph of g(x) is translated 5 units to the left, 2 units down and reflected over the x-axis.

B) The graph of g(x) is translated 5 units to the left, 2 units up and reflected over the y-axis.

C) The graph of g(x) is translated 5 units to the right, 2 units down and reflected over the y-axis.

D) The graph of g(x) is translated 5 units to the right, 2 units up and reflected over the x-axis.

Answer 1

Answer: D

Explanation:

The rule for horizontal translation is f(x-h) is h units to the right and f(x+h) is h units to the left. Since it is in the form f(x-h), and h is five, it is translated 5 units to the right. After this we can see that the vertical translation (in f(x)+k, where k is the vertical translation), we can see that k is positive 2, so it is translated 2 units up. Lastly, we can see that the negative sign is in the form -f(x), which means it is reflected over the x-axis. Hope this helps!