Can someone explain the answer to me? which description matches the transformations y = cos x undergoes to produce y = 2cos (-x) - 4? a. horizontal compression by factor 2, vertical shift by 4 units up, then a reflection across the x-axis b. reflection across the y-axis, vertical stretch by factor 2, then a vertical shift down 4 units c. reflection across the y-axis, vertical shift of 2 units, horizontal shift right by 4 units d. horizontal shift left 1 unit, then vertical shift down by 4 units
horizontal compression by factor 3, vertical stretch by factor 2, then reflection across the x-axis ⇒ answer A
* Lets revise some transformation
- A vertical stretching is the stretching of the graph away from
# If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched
by multiplying each of its y-coordinates by k.
# If k should be negative, the vertical stretch is followed by a reflection
across the x-axis.
- A horizontal compression is the squeezing of the graph toward
# If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally
compressed by dividing each of its x-coordinates by k.
* Lets solve the problem
∵ y = cos x
∵ y = -2 cos 3x
- At first cos x multiplied by -2
∵ y multiplied by -2
∵ 2 > 1
∴ y = cos x is stretched vertically by factor 2
∵ The factor 2 is negative
∴ y = cos x reflected across the x-axis
∴ The function y = cos x stretched vertically with factor 2 and then
reflected across the x-axis ⇒ (1)
∵ cos x changed to cos 3x
∵ x multiplied by 3
∵ 3 > 1
∴ y = cos x compressed horizontally by factor 3
∴ The function y = cos x compressed horizontally by factor 3 ⇒ (2)
- From (1) and (2)
* The function y = cos x has horizontal compression by factor 3,
vertical stretch by factor 2, then reflection across the x-axis to
produce y = -2 cos 3x
Vertical stretch by factor 3 reflections through the x-axis then a vertical shift up 1 unit .