Describe the transformation to the parent function in order to graph the following function, then write the equations of the Vertical and Horizontal Asymptote.

Y = _-2___ + 4
x

To describe the transformation to the parent function in order to graph the given function, we need to analyze the changes made to the parent function, which is y = 1/x.

The given function is Y = (-2/x) + 4.

1. Vertical Stretch/Compression:
The coefficient in front of the parent function (-2) represents a vertical stretch/compression. In this case, the function is vertically compressed by a factor of 2 since the coefficient is less than 1. It means that the graph will be closer to the y-axis compared to the parent function.

2. Vertical Translation:
The constant term added to the parent function (+4) represents a vertical translation. In this case, the function is shifted upward by 4 units.

3. Horizontal Reflection:
There is no horizontal reflection since the coefficient (-2) is negative.

Now, let's determine the equations of the vertical and horizontal asymptotes:

Vertical Asymptote:
The vertical asymptote of a rational function occurs at the values of x that make the denominator zero. In the given function, the denominator is x, so it will equal zero when x = 0. Therefore, the equation of the vertical asymptote is x = 0.

Horizontal Asymptote:
To find the equation of the horizontal asymptote, we need to determine the degrees (highest power of x) in the numerator and denominator. In this case, the degree of the numerator is 0, and the degree of the denominator is 1.

When the degree of the numerator is less than the degree of the denominator, the equation of the horizontal asymptote is y = 0.

Therefore, the equations of the vertical and horizontal asymptotes for the given function are:

Vertical asymptote: x = 0
Horizontal asymptote: y = 0

how about you show some effort on these, and not just a homework dump?

You must have some ideas...