Figure

Use the graph of $f(x) = \tan x$ to graph $g(x) =-\tan\! \left(\! x+\dfrac{\pi }{4}\right)$ .

Figure 78 illustrates the steps used in graphing $g( x) =-\tan\! \left(\! x+\dfrac{\pi }{4} \right)$ .

Begin by graphing

$f( x) =\tan x$ . See Figure 78(a).

Replace the argument

$x$ by

$x+\dfrac{\pi }{4}$ to obtain

$y=\tan\! \left(\! x+\dfrac{\pi }{4} \right)$ , which shifts the graph horizontally to the left

$\dfrac{\pi }{4}$ unit, as shown in Figure 78(b).

Multiply

$\tan\! \left(\! x+\dfrac{\pi }{4} \right)$ by

$-1$ , which reflects the graph about the

$x$ -axis, and results in the graph of

$y =-\tan\! \left(\! x+\dfrac{\pi }{4} \right)$ , as shown in Figure 78(c).