Question

why is it impossible for the graph of the function y=1/x to intersect the horizontal asymptote at the x axis

Answer 1

The graph of the function y=1/x cannot intersect the horizontal asymptote at the x-axis because as x approaches infinity or negative infinity, y approaches zero, but never actually reaches it, which is a fundamental property of asymptotes.

Step-by-step explanation:

The function y = 1/x represents a hyperbola, which has two asymptotes: a vertical asymptote along the y-axis (x=0) and a horizontal asymptote along the x-axis as y approaches zero. By definition, an asymptote is a line that a graph approaches but never actually intersects. Therefore, the graph of the function y=1/x will never intersect the x-axis (horizontal asymptote) because as x gets larger or smaller (towards infinity or negative infinity), the value of y gets closer and closer to zero, but never actually reaches it.

Answer 2

Below.

Step-by-step explanation:

Because y = 1/x is never going to be equal to zero no matter how high you make the value of x ( positive) or how low ( negative).

At these high / low values the function approaches zero but never gets there.

As x --->∞, y ----> 0⁺.

As x ----> -∞, y ----> 0⁻.