Question

Dale graphed the absolute value parent function. Then, he reflected the graph over the x-axis, shifted it four units to the right and three units up. Give the new equation

Answer 1

• i(x) = - |x - 4| + 3

Explanation:

Refer to attached graph

Parent function:

• f(x) = |x|, solid black on the graph

Transformations

1. Reflection over x-axis: f(x) → -f(x)

• g(x) = -|x|, dotted blue on the graph

2. Horizontal shift 4 units to the right: g(x) → g(x - 4)

• h(x) = -|x - 4|, dotted green on the graph

3. Vertical shift 3 units up: h(x) → h(x) + 3

• i(x) = - |x - 4| + 3, solid red on the graph

This is the final function