Final answer:
To trace the curve y = 8/(4-x^2), we start by finding the domain and range. The curve has x-intercepts at x = 2 and x = -2, a y-intercept at y = 2, and is symmetric about the y-axis.
Step-by-step explanation:
To trace the curve y = 8/(4-x^2), we can start by finding the domain and range of the function. The function is defined for all real numbers except when the denominator becomes zero, so we need to exclude x = 2 and x = -2 from the domain. The range of the function is all real numbers except 0.
We can also find the y-intercept by setting x = 0 and solving for y, which gives y = 2. To find the x-intercepts, we set y = 0 and solve for x, which gives x = 2 and x = -2.
Another property of the curve is symmetry. The function is symmetric about the y-axis, meaning that if we replace x with -x in the equation, we get the same equation.