Write the function rule g(x) after the given transformations of the graph of f(x) = -2x
reflection in the y-axis; vertical compression by a factor of 1/4
To obtain the function rule g(x) after the given transformations of f(x) = -2x, we need to apply the transformations in the following order:
1. Reflection in the y-axis: This transformation changes the sign of the x-coordinates of the points on the graph. So, we replace x with -x in the function rule.
f(-x) = -2(-x) = 2x
2. Vertical compression by a factor of 1/4: This transformation squeezes the graph vertically by a factor of 1/4. To achieve this, we multiply the function by 1/4.
g(x) = (1/4)f(-x) = (1/4)(2x) = 1/2 x
Therefore, the function rule g(x) after the given transformations of f(x) = -2x is g(x) = 1/2 x.