What graphical characteristic in the reciprocal function do the zeros of the original function correspond to?
that would be vertical asymptotes.
since 1/0 is undefined
The zeros of the original function of a reciprocal function correspond to vertical asymptotes in the graphical representation. A reciprocal function is defined as f(x) = 1 / g(x), where g(x) is the original function. The zeros of the original function, which are the x-values that make g(x) equal to zero, create vertical asymptotes in the graph of the reciprocal function. Specifically, if g(x) has a zero at x = a, then the reciprocal function has a vertical asymptote at x = a.
The reciprocal function is the inverse of the original function, obtained by taking the reciprocal of each y-coordinate. In the context of the reciprocal of a function, the term "zero" typically refers to the x-values where the original function crosses the x-axis.
The graphical characteristic in the reciprocal function that corresponds to the zeros of the original function is the vertical asymptotes. A vertical asymptote is a vertical line in the graph of the reciprocal function where the function approaches infinity or negative infinity as the x-values approach the x-coordinate of the vertical asymptote.
To find the vertical asymptotes of the reciprocal function, you can follow these steps:
1. Identify the x-values where the original function crosses the x-axis. These are the zeros of the original function.
2. Take the reciprocal of each zero obtained in step 1. This will give you the x-coordinates of the vertical asymptotes in the reciprocal function.
3. Plot the vertical asymptotes on the graph of the reciprocal function. These lines indicate the values where the reciprocal function approaches infinity or negative infinity.
By observing the vertical asymptotes in the graph of the reciprocal function, you can determine the x-values where the original function crosses the x-axis, also known as the zeros of the original function.