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f(x) = 2cos(x). g(x) = graph of sine function which starts at 0 comma 0 and decreases to the minimum of pi over 2 then increases to the maximum 3 pi over 2 then decreases to 2pi where the cycle repeats. Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value. PLEASE ANSWER QUICK FOR BRAINLIEST AWARD

fx 2cosx gx graph of sine function which starts at 0 comma 0 and decreases to the minimum of pi over 2 then increases to the maximum 3 pi over 2 then decreases class=


Answer :

semsee45

Answer:

The maximum y-value for f(x) is y = 2

The maximum y-value for g(x) is y = 3.

The function with the largest maximum y-value is function g(x).

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=2 \cos (x)\\g(x)=3 \sin (x+ \pi)\end{cases}[/tex]

The range of the parent cosine function is:

  • [tex]-1 \leq \cos(x) \leq 1[/tex]

If the parent cosine function has been transformed by a vertical stretch of factor 2, i.e. the function has been multiplied by 2, the range is also multiplied by 2.

Therefore, the range of f(x) is:  

  • [tex]-2 \leq 2\cos(x) \leq 2[/tex]

and so the maximum y-value for f(x) is y = 2.

The range of the parent sine function is:

  • [tex]-1 \leq \sin(x) \leq 1[/tex]

If the parent sine function has been transformed by a vertical stretch of factor 3, i.e. the function has been multiplied by 3, the range is also multiplied by 3.

Therefore, the range of g(x) is:  

  • [tex]-3 \leq 3 \sin (x + \pi) \leq 3[/tex]

and so the maximum y-value for g(x) is y = 3.

As 3 > 2, the function with the largest maximum y-value is function g(x).

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