Describe the difference between the graph of:
y - 3 = -tan( -2x + 180°) and y = tan(x)

Question

Describe the difference between the graph of:
y - 3 = -tan( -2x + 180°) and y = tan(x)

anonymous · Answer

The general form of the tangent function could be written as
$$y=a\tan \big(b(x-c)\big)+d$$
where $a$ is a scaling factor, $b$ is related to the period of the function (with $p=\dfrac{\pi}{b}$), $c$ is a horizontal shift of $c$ units left (if positive) or right (if negative), and $d$ is a vertical shift of $d$ units up (if positive) or down (if negative).

Try writing $y-3=-\tan\left(-2x+180^\circ \right)$ in this general form.

anonymous · Answer

ok so would say the differences then?

anonymous · Answer

how would **

anonymous · Answer

The general form of your given function is
$$y=-\tan\big(-2(x-90^\circ)\big)+3$$
So you have $a=-1$, $b=-2$, $c=90^\circ$, and $d=3$.

$a$ is the scaling factor. In this case, it's negative, so the change made to the graph of $\tan x$ is a reflection across the x-axis.
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