Question

Describe the transformation from the parent function to y=-|x+3|-5.

a) The function is a vertical shift 5 units down and a horizontal shift 3 units to the left.
b) The function is a vertical shift 5 units up and a horizontal shift 3 units to the right.
c) The function is a reflection across the x-axis, followed by a vertical shift 5 units down and a horizontal shift 3 units to the left.
d) The function is a reflection across the y-axis, followed by a vertical shift 5 units down and a horizontal shift 3 units to the left.

Answer 1

The transformation from the parent function to
`\(y = -|x+3|-5\)` can be described as: The function is a reflection across the x-axis, followed by a vertical shift 5 units down and a horizontal shift 3 units to the left.

The answer is option ⇒c

Step-by-step explanation:

Here's a step-by-step breakdown of the transformation:

1. Reflection across the x-axis:

• The negative sign in front of the absolute value function indicates a reflection across the x-axis. This means that the portion of the graph that would be above the x-axis in the parent function is now below the x-axis in the transformed function.

2. Vertical shift 5 units down:

• The "-5" at the end of the function represents a vertical shift downwards. Each point on the graph is moved 5 units downward from its corresponding point on the parent function.

3. Horizontal shift 3 units to the left:

• The "+3" inside the absolute value function represents a horizontal shift to the left. Each point on the graph is moved 3 units to the left from its corresponding point on the parent function.

By combining these transformations, we can see that the graph of the transformed function is obtained by first reflecting the parent function across the x-axis, then shifting it 5 units down and 3 units to the left.

The answer is option ⇒c