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 + 6| + 3
c) 𝑦 =− |𝑥 − 6| + 3
d) 𝑦 = |𝑥 − 6| + 3

Answer 1

The correct option is d) 𝑦 = |𝑥 − 6| + 3.

When we reflect the graph of 𝑦 = |𝑥| across the x-axis, it becomes 𝑦 = −|𝑥|.
When we shift it vertically up 3 units, it becomes 𝑦 = −|𝑥| + 3.
When we shift it horizontally to the left 6 units, it becomes 𝑦 = −|𝑥 - 6| + 3.
Adding the absolute value function back to the equation gives 𝑦 = |𝑥 - 6| + 3.