determine the equation of the image y = root x in each case
a) its graph is compressed horizontally by a factor of 1/4
b)its graph is expanded vertically by a factor of 2
To determine the equation of the image y = √x in each case, we need to apply the appropriate transformations to the original equation.
a) When the graph is compressed horizontally by a factor of 1/4, it means that the x-values are being multiplied by 1/4. This compression can be achieved by replacing x with 4x in the original equation.
So, the equation of the image when the graph is compressed horizontally by a factor of 1/4 is:
y = √(4x)
b) When the graph is expanded vertically by a factor of 2, it means that the y-values are being multiplied by 2. This expansion can be achieved by multiplying the entire equation by 2.
So, the equation of the image when the graph is expanded vertically by a factor of 2 is:
2y = √x
These transformations modify the original equation to obtain the equations of the respective images.