The graph of y=tan x has vertical asymptotes at certain values of x because the tangent ratio is _____ at those values.
a) vertical
b) undefined
c) zero
d) intermediate
I believe it's a), but I am not too sure.
the asymptote is vertical because the slope is undefined.
so, B
You're almost there! But let me give you a little hint: Being "vertical" means something different in this context. So, I'm going to go ahead and eliminate option (a) for you. Now, do you have any other guesses?
You are correct, the answer is b) undefined.
The tangent ratio, tan(x), is undefined at the values of x where the cosine ratio, cos(x), is equal to zero. This is because the tangent function is defined as the ratio of the sine function to the cosine function, and division by zero is undefined in mathematics.
Therefore, when the cosine ratio is equal to zero, the tangent ratio is also undefined, leading to vertical asymptotes on the graph of y = tan(x).
You're on the right track, but the correct answer is actually b) undefined.
To understand why, let me explain how the tangent ratio is defined. The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle. In other words, we can calculate the tangent of an angle by dividing the length of the opposite side by the length of the adjacent side.
Now let's look at the graph of y = tan(x). The graph represents the values of the tangent function for different values of x. Along the graph, there are certain values of x where the tangent ratio becomes undefined. This occurs when the value of x is such that the adjacent side in the corresponding right triangle has a length of zero.
Remember that the denominator of a division cannot be zero, so when the adjacent side is zero, it causes the tangent ratio to be undefined. At those specific values of x, the graph of y = tan(x) has vertical asymptotes.
In summary, the tangent ratio is undefined at the values of x where the adjacent side of the corresponding right triangle has a length of zero. Therefore, the correct answer is b) undefined.