199k views
3 votes
What is the range of the function y = -3cosx + 1?

-4 ≤ x ≤ 4
-3 ≤ x ≤ 3
-3 ≤ x ≤ 4
-2 ≤ x ≤ 4

User PaulR
by
7.8k points

1 Answer

3 votes

Answer:


-2\leq x\leq 4

Explanation:

Recall that the function cos(x) shows an oscillating curve between the values -1 and 1 on the vertical axis (the Range of this goes therefore between y = -1 to y=1).

Now, when you multiply this trig function by "-3", its amplitude increases, and therefore it will be now oscillating between the values y=-3 and y=3.

if to this, you now add 1 (to complete the function: f(x) = -3 cos(x) +1, you are translating the full function one unit up. Then the new function will be still oscillating, but between the values y=-2 and y = 4 (the previous ones shifted up by 1 unit)

Therefore, the answer to the question is:

Range of f(x) is {
-2\leq x\leq 4}, which coincides with your last answer choice.

User Plowman
by
8.4k points

Related questions

asked Jan 4, 2024 77.6k views
Akinuri asked Jan 4, 2024
by Akinuri
7.3k points
1 answer
0 votes
77.6k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories