Question

What equation(s) represent the vertical asymptote(s) of the graph of y = 1/x^2 - 4? J) x = -4 and x = 4 K) x = - 2 and x = 2 L) x = 0 only M) x = 2 only N) x = 4 only

Answer 1

K) x = - 2 and x = 2

Explanation:

Vertical asymptotes occur when the denominator of a fraction equals to zero, but the numerator does not. In the case of y = 1/x^2 - 4, the denominator is x^2 - 4.

The equation x^2 - 4 = 0 represents the points at which the denominator equals to zero, so we can find the solutions for x by solving this equation:

x^2 - 4 = 0

x^2 = 4

x = ±2

So x = 2 and x = -2 represents the vertical asymptote of the graph of y = 1/x^2 - 4

This means that the graph of the function approaches zero as x approaches 2 and -2 from the left and right respectively, but it never touches the x-axis at those points.