Question

What are the horizontal and vertical asymptotes of the graph of x2 – 1 ?

A y=1, x=1, and x=3
B y=-1 and x=1 and x=-1
C y=-1 and x=-5
D y=-1, x=-1, and x=4

Answer 1

The quadratic function x^2 – 1 does not have horizontal or vertical asymptotes. Thus, all given answer options are incorrect.

Step-by-step explanation:

The student's question is about finding the horizontal and vertical asymptotes of a given function. The function presented is x2 – 1, which is a quadratic function and does not inherently have asymptotes as it is a parabola. Therefore, the answers provided (A, B, C, D) which suggest this function has asymptotes are incorrect.

Asymptotes are typically associated with rational functions, which have a variable in the denominator, and certain transcendental functions like logarithmic and exponential functions. For quadratic functions like the one given, you may instead discuss features such as the vertex, axis of symmetry, and x/y-intercepts instead of asymptotes.