Describe the transformation in f(x)= -4x from its linear parent function. is it reflection and rotation?
no rotation. reflection and scaling.
y = x
scale by 4: y = 4x
reflect in x-axis: y = -4x
The function f(x) = -4x represents a linear function with a negative slope. The parent function is the basic linear function f(x) = x.
To describe the transformation from the linear parent function to f(x) = -4x, we need to focus on the coefficient of x, which is -4.
The negative sign in front of 4 indicates a reflection across the x-axis. Reflecting a function across the x-axis flips it upside down. So, this is a reflection transformation.
There is no rotation involved in this transformation since the function remains in the same orientation as the parent function.
In summary, the transformation represented by f(x) = -4x is a reflection across the x-axis of the linear parent function f(x) = x.
To describe the transformation in the function f(x) = -4x from its linear parent function, we need to compare it to the standard linear function y = mx.
The parent function is y = x, which is a linear function with a slope of 1.
In f(x) = -4x, we see that the coefficient in front of x is -4, which means the slope of the function is -4.
Therefore, the transformation in the function f(x) = -4x from its linear parent function is a vertical stretch by a factor of 4.
This means that every y-value in the original linear function is multiplied by -4 in order to obtain the corresponding y-value in the transformed function.
It is important to note that this transformation does not involve reflection or rotation. Instead, it only causes a vertical stretching or compressing of the parent function.