Question
Find the equation for the curve y = cos (x) is shifted a distance of pi/3 to the left, reflected in the x-axis, translated 6 units downward, then stretched by a factor of 4.
Answers
GPT 3.5
To shift the curve y = cos(x) a distance of π/3 to the left, we substitute (x + π/3) for x:
y = cos(x + π/3)
To reflect the curve in the x-axis, we substitute (-y) for y:
-y = cos(x + π/3)
To translate the curve 6 units downward, we subtract 6 from y:
-y - 6 = cos(x + π/3)
To stretch the curve by a factor of 4, we multiply y by 4:
-4(y + 6) = cos(x + π/3)
Therefore, the equation for the curve y = cos(x) shifted a distance of π/3 to the left, reflected in the x-axis, translated 6 units downward, then stretched by a factor of 4 is:
-4(y + 6) = cos(x + π/3)
y = cos(x + π/3)
To reflect the curve in the x-axis, we substitute (-y) for y:
-y = cos(x + π/3)
To translate the curve 6 units downward, we subtract 6 from y:
-y - 6 = cos(x + π/3)
To stretch the curve by a factor of 4, we multiply y by 4:
-4(y + 6) = cos(x + π/3)
Therefore, the equation for the curve y = cos(x) shifted a distance of π/3 to the left, reflected in the x-axis, translated 6 units downward, then stretched by a factor of 4 is:
-4(y + 6) = cos(x + π/3)