Question

Name the transformations of the next equation y=3(x+6)-5

A Horizontal shift 6 right Vertical Shift down 5 Stretch by a factor of 3 Reflection over the x axis

B Horizontal shift 6 right Vertical Shift up 5 Shrink by a factor of 3 Reflection over the x axis

C Horizontal shift: 6 left Vertical Shift 5 down Stretch by a factor of 3 No reflection


D Horizontal shift: 6 left Vertical Shift 5 up Stretch by a factor of 3 No reflection

Answer 1

The equation y = 3(x + 6) - 5 represents option C. horizontal shift 6 to the right, a vertical shift downward 5 units, a stretch by a factor of 3, and no reflection over the x-axis.

Step-by-step explanation:

The equation y = 3(x + 6) - 5 represents several transformations:

1. A horizontal shift 6 to the right: The original equation y = x is shifted 6 units to the right. So the new equation becomes y = x + 6.
2. A vertical shift downward 5 units: The original equation y = x + 6 is shifted downward 5 units. So the new equation becomes y = x + 6 - 5 = x + 1.
3. A stretch by a factor of 3: Each y-coordinate of the original equation y = x + 1 is multiplied by 3. So the new equation becomes y = 3(x + 1).
4. No reflection over the x-axis.