Match each function with its graph in choices A–F.

Question

y = tan (x - π )

A. B. C.

D. E. F.

Accepted Answer

Graph. The following function considering only one period Y equals 10 X minus pi divided by three. And we're also given a coordinate plane here to graph our equation on. Now, tangent works a little bit strange for a tangent, we first need to find our asymptotes. So in a normal tangent graph, the asymptotes occur at pi divided by two and negative pi divided by two. Since our function is 10 X minus pi divided by three, I will replace our X with X minus pi divided by three. Now, we can simplify to BX by adding pi divided by three to both sets or our value on the left, we would get negative pi divided by six. For a value on the right, we would get five pi divided by six. We now have our two asymptotes. Now with a tangent function, the midpoint of the function is halfway between our two asymptotes. So let's find our midpoint of our ascent toes. That would be negative pi divided by six plus five pi divided by six, all divided by two. That gives us four pi divided by six, all divided by two, which results in pi divided by three. This is actually our X intercept, our X intercept then will be pi divided by 30. No, we have one more thing to do, which is to find two more points on our graph. To find this, we need to see where Y is equals to one. And why is equals to negative one. This will be very easy values to find. We can now say that we have our Asymptote plus our fifth point divided by two. This gives us the midpoint of our X intercept and the Asymptote. So we can say negative I divided by six plus our X intercept all divided by two, five pi divided by six plus pi divided by three, all divided by two. Those will give us either Y one or Y equals negative one when plugged in. And in fact, since our larger number, it's on the right side for us that one will be a positive, smaller number will be our negative. Now we get X equals negative pi divided by six plus pi divided by three that gives us pi divided by six all divided by two or pi divided by 12. Similarly, for the other one, we would get seven pi divided by 12. We now have three points and two as totes. We can put on our graph divided by 30 seven pi divided by 12 1 and pi divided by 12 negative one. We can now plot this pi divided by 30 seven pi divided by 12 as the one and pi divided by 12, negative one. And we have two asymptotes. So I will put right there at five pi divided by six and negative pi divided by six. Finally, we just draw a smooth curve between the points from the Asymptote from there. Follow our points up and to the right, this is our graph 10 X plus pi divided by three. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

Match each function with its graph in choices A–F.

y = tan (x - π )

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

Key Concepts

Tangent Function Properties

Phase Shift

Graphing Trigonometric Functions

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