Which of the following describes the graph of y = |x| after it has been reflected across the

Question

x-axis, shifted vertically up 3 units, and shifted horizontally to the left 6 units?
a) y = x + 6 + 3
b) y=x+61 +3
c) y = x 6 + 3
d) y = x 6 + 3

Answer 1

The correct answer is c) y = x - 6 + 3.

When a graph is reflected across the x-axis, the sign of the y-coordinate is changed. So, the equation becomes y = -|x|.
When the graph is shifted vertically up 3 units, this means adding 3 to the y-coordinate. So, the equation becomes y = -|x| + 3.
When the graph is shifted horizontally to the left 6 units, this means subtracting 6 from the x-coordinate. So, the equation becomes y = -|x-6| + 3.
Simplifying, we get y = x - 6 + 3, which is option c).