y = 3cos(x-1)
Shift along x:
Shift along y:
Kind of reflection:
shift x: 1 right
shift y: 0
reflection: none
What kind of reflections are the following trig functions?
y = 3cos(x-1)
y = sin(-3x+3)
y = -2sin(x)-4
To determine the shift along the x-axis, we need to compare the given equation to the general form of a cosine function: y = A*cos(B(x-C)) + D.
In the given equation, y = 3*cos(x-1), the value of C is 1. So, there is a shift along the x-axis of +1 unit, to the right.
To determine the shift along the y-axis, we need to look at the value of D in the general form of the cosine function. In this case, the value of D is 0, which means there is no shift along the y-axis (up or down).
To find the kind of reflection, we need to compare the given equation to the general form of a cosine function. In this case, there is no reflection because the coefficient of the cosine function (A) is positive (+3). If A were negative, then there would be a reflection about the x-axis.
So, to summarize:
- There is a shift along the x-axis of +1 unit to the right.
- There is no shift along the y-axis.
- There is no reflection.