Question

Which description matches the transformations y = cosx undergoes to

produce y = -3cos(x)+1?
A. Horizontal shift left 3 units, then vertical shift up by 1 unit
B. Horizontal compression by factor 3, vertical shift by 1 unit up, then a reflection across the x-axis
C. Vertical stretch by factor 3, reflection across the x-axis, then a
vertical shift up 1 unit
D. Reflection across the y-axis, vertical shift up by 1 unit, horizontal shift right by 3 units

Answer 1

C.

Explanation:

The parent function is y = cos(x).

When we have y = cos(x) + 1, this tells us that the graph has been shifted up by 1.

When we have y = -cos(x), this tells us that the graph has been reflected across the x-axis.

When we have y = 3cos(x), this tells us that the graph has been vertically stretched by a factor of 3.

All together, the answer is C.

Notes:

y = 3cos(x) would be a vertical stretch, while y = cos(3x) would be a horizontal compression.

y = -cos(x) is a reflection across the x-axis, while y = cos(-x) would be a reflection across the y-axis.