Question 1203774


{{{ j(x)=tan(pi/4x)}}}


use the form {{{ j(x)=a*tan(bx-c)+d }}}to find the amplitude, period, phase shift, and vertical shift

in your case, a general equation is {{{ y=A*tan(Bx)}}}

We can identify horizontal and vertical stretches and compressions using values of  {{{ A}}} and {{{  B}}}. The horizontal stretch can typically be determined from the period of the graph. With tangent graphs, it is often necessary to determine a vertical stretch using a point on the graph.

Because there are {{{ no}}} maximum or minimum values of a tangent function, the term amplitude cannot be interpreted as it is for the sine and cosine functions. Instead, we will use the phrase {{{ stretching/compressing}}} factor when referring to the constant {{{  A}}}.

The stretching factor is  {{{ abs(A)}}}
 
The period is {{{  P=pi/abs(B)}}}
 .
The asymptotes occur at  {{{ x=pi/2abs(B)+(pi/abs(B))k}}} where  {{{ k}}} is an integer.

stretching/compressing factor: {{{ none}}}

period: {{{ P=pi/abs(pi/4)=4}}}

phase shift: {{{ none}}}

vertical shift: {{{ none}}}

horizontal asymptotes:{{{  none}}}

vertical asymptotes: {{{ 2+4k}}}

in two periods, you have asymptotes:

{{{ x=2}}}

{{{ x=-2}}}

oblique asymptotes: {{{ none}}}


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