What is the range of the function y = -3cosx + 1? -4 ≤ x ≤ 4 -3 ≤ x ≤ 3 -3 ≤ x ≤ 4 -2 ≤ x ≤ 4

Question

What is the range of the function y = -3cosx + 1?

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

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Harper 2 weeks 2021-09-12T05:44:50+00:00 1 Answer 0

Answers ( )

    0
    2021-09-12T05:46:08+00:00

    Answer:

    -2\leq x\leq 4

    Step-by-step 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.

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