Equation that represents a rotation of the linear parent function??
To represent a rotation of the linear parent function, we need to introduce a transformation called a rotation. A basic rotation in mathematics involves rotating a point or a function by a certain angle around a fixed point.
The linear parent function is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. To rotate this linear parent function, we can use a rotation matrix.
A rotation matrix is a 2x2 matrix that represents a rotation in a coordinate plane. For a counterclockwise rotation of angle θ around the origin, the rotation matrix is:
R = [cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
To apply this rotation matrix to the linear parent function, we need to multiply the matrix with the coordinates of the points on the function. Let's assume we want to rotate the function counterclockwise by an angle θ.
The coordinates (x, y) of the original linear parent function become:
[x', y'] = [x, y] * R
Now, we can substitute the coordinates (x, y) with (x', y') in the linear parent function equation:
y' = m*x' + b
This represents the equation of the rotated linear function.
Note: It's important to convert the angle θ to radians if your calculator functions in radians.
Keep in mind that rotating a linear function using a rotation matrix will generally result in a non-linear function.