Question

Choose the function that represents the graph of the transformation of f(x) = |x| that opens down and has a vertex of (3,2)

f(x) = |x - 3| - 2
f(x) = -|x - 3| + 2
f(x) = |x + 3| + 2
f(x) = -|x + 3| + 2

Answer 1

f(x)=-|x-3|+2

Negative before the abs value inverts the graph and it moves right 3 and up 2

Answer 2

f(x) = -|x - 3| + 2.

Explanation:

f(x) = |x| is shaped like a V and the vertex is at (0, 0). f(x) = -|x| is a reflection in the x-axis so will be an inverted V , opening down. f(x) = - |x - 3| will be the -|x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex to (3, 2) it will move upwards 2 units.

So it is f(x) = -|x - 3| + 2.