identify how the graph is shifted from that of the parent function.\n$y = \\tan(x)+7$\n7 units up\n7 units…

identify how the graph is shifted from that of the parent function.\n$y = \\tan(x)+7$\n7 units up\n7 units down\n7 units left\n7 units right\ndone\n$y = \\cot(x - 3)$\n3 units up\n3 units down\n3 units left\n3 units right\ndone

identify how the graph is shifted from that of the parent function.\n$y = \\tan(x)+7$\n7 units up\n7 units down\n7 units left\n7 units right\ndone\n$y = \\cot(x - 3)$\n3 units up\n3 units down\n3 units left\n3 units right\ndone

Answer

Answer:

  1. For $y = \tan(x)+7$: A. 7 units up
  2. For $y=\cot(x - 3)$: D. 3 units right

Explanation:

Step1: Recall vertical - shift rule

For a function $y = f(x)+k$, if $k>0$, the graph of $y = f(x)$ is shifted $k$ units up. For $y=\tan(x)+7$, compared to $y = \tan(x)$, here $k = 7>0$, so it is shifted 7 units up.

Step2: Recall horizontal - shift rule

For a function $y = f(x - h)$, if $h>0$, the graph of $y = f(x)$ is shifted $h$ units to the right. For $y=\cot(x - 3)$, compared to $y=\cot(x)$, here $h = 3>0$, so it is shifted 3 units to the right.