Functions and transformation

Question

The graph of f (x) = |x| is reflected across the x-axis, moved 2 units to the right and 7 down. What is the function?

Answer 1

Greetings Tonia,

The graph function is as such: The original graph f (x) = |x| is a "V-shaped" graph with the vertex starting at the origin (0,0).

When reflected it remains the same, but negatively.

When moving 2 units to the right, it remains on the x-axis, which the graph function is now f (x) = -|x-2|

When moving 7 units down, it remains on the y-axis, which the graph function is now f (x) = -|x-2| -7.

Answer: f (x) = -|x-2|-7

There is also a vertex formula of f (x) = a|x-h|+k, where (h,k) is the vertex. A is the amplitude (reflection, stretch/shrink vertically), h for horizontal shift, and k for vertical shift.