2. find the range of y = 7 + sec x.\na) (-∞,6 ∪ 8,∞)\nb) (-∞,-7 ∪ 7,∞)\nc) 6,8\nd) (-∞,-1 ∪ 1,∞)
2. find the range of y = 7 + sec x.\na) (-∞,6 ∪ 8,∞)\nb) (-∞,-7 ∪ 7,∞)\nc) 6,8\nd) (-∞,-1 ∪ 1,∞)
Answer
Explanation:
Step1: Recall range of secant function
The range of $y = \sec x$ is $(-\infty,-1]\cup[1,\infty)$.
Step2: Find range of $y = 7+\sec x$
If $y_1=\sec x$ and $y = 7 + y_1$, when $y_1\leq - 1$, then $y=7 + y_1\leq7-1 = 6$. When $y_1\geq1$, then $y=7 + y_1\geq7 + 1=8$. So the range of $y = 7+\sec x$ is $(-\infty,6]\cup[8,\infty)$.
Answer:
A. $(-\infty,6]\cup[8,\infty)$