Write an equation for a function at has a graph with the given characteristics. the shape of y=|x| is reflected across the y-axis. this graph is then vertically stretched by a factor of 1.5. Finally, the graph is shifted 4 units downward.

reflected: y = |-x|

stretched: y = 1.5|-x|
shifted: y = 1.5|-x| - 4

However, since |-x| = |x| the reflection has no effect.

To write the equation of a function with the given characteristics, we need to consider the transformations applied to the initial function y = |x|.

First, the graph is reflected across the y-axis, which means the positive and negative parts of the graph are swapped. This can be achieved by placing a negative sign in front of the function.

Second, the graph is vertically stretched by a factor of 1.5. This means the y-values of the function are multiplied by 1.5. To accomplish this, we multiply the function by 1.5.

Finally, the graph is shifted 4 units downward, meaning it is translated down along the y-axis. This is achieved by subtracting 4 from the function.

Combining all these transformations, we get the equation of the function as follows:

f(x) = -1.5| x | - 4

This equation represents the graph of y = |x| reflected across the y-axis, vertically stretched by a factor of 1.5, and shifted 4 units downward.