Example 3. Sketch the graph y = -3 tan 2x.
Your Turn: Sketch the graph of y = 2 tan 2x.
Your Turn: Sketch the graph of y = -tan(x/2).

Question

Example 3. Sketch the graph y = -3 tan 2x. Your Turn: Sketch the graph of y = 2 tan 2x. Your Turn: Sketch the graph of y = -tan(x/2).

SnapAndSolve AI · Accepted Answer

The graph of y = -3 tan 2x is a vertically stretched and reflected version of the basic tangent function. The period is π/2, and the graph has vertical asymptotes at x = ±π/4, ±3π/4, etc. The graph passes through the origin and has a slope of -3 at the origin.
The graph of y = 2 tan 2x is a vertically stretched version of the basic tangent function. The period is π/2, and the graph has vertical asymptotes at x = ±π/4, ±3π/4, etc. The graph passes through the origin and has a slope of 2 at the origin.
The graph of y = -tan(x/2) is a horizontally stretched and reflected version of the basic tangent function. The period is 2π, and the graph has vertical asymptotes at x = ±π, ±3π, etc. The graph passes through the origin and has a slope of -1 at the origin.

Example 3. Sketch the graph y = -3 tan 2x. Your Turn: Sketch the graph of y = 2 tan 2x. Your Turn: Sketch...