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3 years ago

How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function?

Mathematics

2 answers:

Alla [95]3 years ago

6 0

The graph has been moved 3 units downward, making the range change. The range of f(x) is [-5,5], while the range of g(x) is [-8,2]. The picture is of both functions. f(x) is blue, g(x) is red.

inna [77]3 years ago

5 0

Answer:

[-8,2]

Step-by-step explanation:

We are given that the function f(x) is transformed to the function g(x), where,

$f(x) =-5 \cos 2x$ and $g(x) =-5 \cos 2x-3$ .

Since, the range of $\cos x$ is [-1,1].

Thus, the range of $a\cos bx$ is {-a,a].

So, the range of $f(x) =-5 \cos 2x$ is [-5,5].

As, we are translating the function f(x) 3 units downward to get g(x).

The graph of the function is shifted 3 units down.

So, the range of g(x) will be [-5-3,5-3] = [-8,2].

Hence, the range of $g(x) =-5 \cos 2x-3$ is [-8,2].

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Answer:

Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance

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Step-by-step explanation:

Step(I):-

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Step(ii):-

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Alternative Hypothesis:-

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where

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Answer:

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