Graph each function over a one-period interval. See Examples 1...

Question

Graph each function over a one-period interval. See Examples 1–3.

y = 2 tan x

Accepted Answer

Graph. The following function considering only one period Y equals four tangent X where we also have a coordinate plane right below to graph our function on. Now to grab this, we need to find the asymptotes and points of tangent X by default tangent X has asymptotes at pi divided by two which is negative and I divided by two positive. Now, our function for tangent X is just stretched in the Y direction because we only have a vertical stretch. Our asymptotes will remain the same negative pi divided by two and positive pi divided by two. Now, we can find three points on our tangent graph. We can first find the midpoint of the ascent toes. This will give us the very middle of our tangent graph which will to note as midpoint, this is also our X intercept because we're not shifting upwards or downwards. We will take our asymptotes, add them together and divide them by two. This gives us our X coordinate. This will be zero, divided by two which is zero. We then have a point at 00. We can now find two more points by finding the midpoint between our ex innocent and our Asymptote, let's see, we have negative pi divided by two plus zero, divided by two and pi divided by two plus zero, divided by two. Those are two different X values we have. Now we would get X equals negative pi divided by two, all divided by two to get negative pi divided by four. And the same on the other side, it's positive pi divided by four. Now because we have an amplitude or, or why that is gonna change are why then will be negative four and positive four. Normally with a tangent function, our amplitude would be one, meaning it would be negative one and positive one. But since we have a stretch of four, these turn into negative four and positive four giving us two points of negative pi divided by four, negative four and pi divided by four, positive four, we can now grasp everything on our plane. Here, we have two asymptotes negative pi divided by two, I divided by two. And we have our points 00, I divided by 44, negative P divided by four, negative four. Just drawing a smooth curve will give us the graph Y equals four tangent X OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Graph each function over a one-period interval. See Examples 1–3.
y = 2 tan x

Key Concepts

Periodicity of Trigonometric Functions

Transformation of Functions

Asymptotes in Tangent Functions

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