Complete the statement by referring to a graph of a trigonometric function. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
(a) As x (-3ð/4)+, tan(x)
To complete the statement, we need to determine the behavior of the tangent function as x approaches (-3π/4)+ (or -3π/4 from the right side).
To find this out, we can refer to the graph of the tangent function. The tangent function is periodic with a period of π, meaning the pattern repeats every π units. However, the given value (-3π/4) is within the first period, so we only need to focus on the behavior in that interval.
If we draw the graph of the tangent function in the interval (-π/2, π/2), we can see that the tangent function has a vertical asymptote at x = π/2 and x = -π/2. As x approaches these vertical asymptotes from the right side, the tangent function approaches positive and negative infinity, respectively.
Since (-3π/4) falls within this interval, as x approaches (-3π/4)+, the tangent function approaches the vertical asymptote at x = -π/2. Therefore, the answer is -INFINITY.