Question

Which is an example x-intercept of the graph of the function y=tan(x-(5pi/6))

Answer 1

Answer:

D?

Step-by-step explanation:

Answer 2

Answer: x = 5π/6

Explanation:

1) Given function:

$y=tan(x- \frac{5 \pi }{6} )$

2) x-intercept are the roots of the function, i.e. the solution to y = 0

3) to find when y = 0, you can either solve the equation or look at the graph.

4) Solving the equation you get:

y = 0 ⇒ tan(x - 5π/6) = 0 ⇒ x - 5π/6 = arctan(0)

arctan(0) is the angle whose tangent is zero,so this is 0

⇒ x - 5π/6 = 0 ⇒ x = 5π/6.

Then, one example of an x-intercept is x = 5π/6, which means that when x = 5π/6, the value of the function is 0.

Since, the tangent function is a periodic function, there are infinite x-intecepts, that is why the questions asks for one example and not all the values.

You can verify by replacing the value x = 5π/6 in the given function:

y = tan (5π/6 - 5π/6) = tan(0) = 0.