S1HAYGbeCh6ababystaa
contestada

Which of the following is the graph of f(x) = 5 cos (2x)?

A.) graph with points 0, 5 and pi over 4, 0 and pi over 2, negative 5 and 3 pi over 4, 0 and pi, 5
B.) graph with points at 0, 0 and pi over 4, negative 3 and pi over 2, 0 and 3 pi over 4, 3 and pi, 0
C.) graph with points 0, negative 5 and pi over 4, 0 and pi over 2, 5 and 3 pi over 4, 0 and pi, negative 5
D.) graph with points at 0, 5 and pi over 4, 2 and pi over 2, negative 1 and 3 pi over 4, 2 and pi, 5

Respuesta :

Mindaka

Answer: A) graph with points (0, 5) and (π/4, 0) and (π/2, -5) and (3π/4, 0) and (π, 5).


First of all, consider that the function f(x) is a transformation of the cosine function, generically given by the formula:

y = A·cos(ωx + Ф) + B

 

In our case, Ф and B are zero, which means that there is no vertical or horizontal shift. What changes is the amplitude A and the period given by T = 2π/ω.

 

The cosine function has a period of 2π, a range [-1, 1] starts at (0, 1) where it has a maximum, intersects the x-axis on x = π/2 and 3π/2, has a minimum at (π, -1) and another maximum at 2π.

 

Similarly, the function f(x) has a period of T = 2π/2 = π, which means that it completes a cycle in half the space of the cosine, and an amplitude A = 5, which means that it is stretched in a range [-5, 5]. Therefore, we can say that it starts at (0, 5) where it has a maximum, intersects the x-axis on x = π/4 and 3π/4, has a minimum at (π/2, -5) and another maximum at π.

 

The option describing this behavior is option A.

Ver imagen Mindaka

The correct graph is; Option A: graph with points 0, (5 and π/4), (0 and π/2), (-5 and 3π/4), (0 and π/5)

How to Interpret Trigonometric Graphs?

We are given the function;

f(x) = 5 cos (2x)

Now, we know that the general form of cosine graph function is;

y = A cos(ωx + Ф) + B

Thus, we can see that the function f(x) is a transformation of the cosine function.

Comparing our given function to the general one above, It is clear that Ф and B are zero.

Thus, we can say that there is no vertical nor horizontal shift.

However, the amplitude A could change and the period is given by;

T = 2π/ω.

The cosine function has a period of 2π, a range [-1, 1] starts at (0, 1) where it has a maximum, intersects the x-axis on x = π/2 and 3π/2, has a minimum at (π, -1) and another maximum at 2π.

Our function f(x) has a period of T = 2π/ω = 2π/2 = π.

Thus, our given function completes a cycle in half the space of the cosine with an amplitude of; A = 5,

Thus, we can say that it is stretched in a range [-5, 5] and so it starts at (0, 5).

where;

It has a maximum.

It intersects the x-axis on x = π/4 and 3π/4.

It has a minimum at (π/2, -5) and another maximum at π.

Thus graph with points 0, (5 and π/4), (0 and π/2), (-5 and 3π/4), (0 and π/5)

Read more about Trigonometric graphs at; https://brainly.com/question/24329125

#SPJ5

Otras preguntas