The graph of y=tan[1/4(x-pi/2)]+1 is shown. what is the period of the function?
4pi
where are the asymptotes of the function?
5pi/2+4npi

what are the x-intercepts of the functions?

answer idk can you me with this that knows

worth 20 points

answer:

the n-th asymptote will be find in . the number n is a whole number.

the x-intersect of the function are

step-by-step explanation:

consider the generic form of the tangent:

where a is amplifying/dilating factor of the curve and b is the shifting of the curve from its original form.

to calculate the period of the tangent, the formula is:

substituting:

from the graph, it can be seen that the asymptotes   are between (-2π) and (-π), so the asymptote of the left hand side is on the line . the one on the right hand side can be found by adding the period:

.

since the tangent function has a period, the next asymptote will be find by adding 4π (period of the function). therefore, the n-th asymptote will be find in .

the intercept is found when the y=tan[1/4(x-pi/2)]+1 is equal to zero:

the angle at which that expression is zero is at 45 + 180 = 225, which is 5. by adding 4nπ, the n-th x-intersect can be found. therefore, the x-intersect of the function are

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2