Final answer:
The student requested to sketch the function f(x) = 1/(x^2 - 1), which has a hyperbolic shape with vertical asymptotes at x = 1 and x = -1, and a horizontal asymptote at y = 0.
Step-by-step explanation:
The student is asking to sketch the graph of the function f(x) = 1/(x^2 − 1). To graph this function, identify the important features such as its asymptotes, intercepts, and end behavior.
This function has vertical asymptotes at x = 1 and x = -1 where the denominator is zero, and a horizontal asymptote at y = 0 as the value of x approaches infinity. There is no x-intercept because the output value is never zero.
The y-intercept occurs at (0, -1). The function is positive when x < -1 and when x > 1, and negative between these two values. The end behavior is such that as x approaches plus or minus infinity, the function approaches zero.
The graph of this function will show hyperbolic branches in the first and third quadrants.