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olchik [2.2K]
3 years ago
9

Determine o período e o conjunto imagem, construindo o gráfico de um período completo para cada função dada.a) por f(x) = 1+ 4 s

en x.b) por f(x) = 2sen (x-3)

Mathematics
1 answer:
nataly862011 [7]3 years ago
7 0

Answer:

The given functions are

f(x)=1+4sinx

f(x)=2sin(x-3)

The sine function has a standard period of 2 \pi by definition. However, this might change if we use a factor as coefficient of the x-varible, but in this case we don't have that.

Therefore, the period of both trigonometric functions is 2 \pi.

Now, the images of each function is the y-variable set values that defines each function.

So, the function f(x)=1+4sinx has an image defined by the set [-3,5]. It's impotant to notice that the range of a standard function is [-1,1], however, in this case, the function was shifted 1 unit up and it was streched by a factor of 4, that's why the standard image changes to [-3,5].

About the second function f(x)=2sin(x-3), the image set is [-2,2], because the function was streched by a factor of 2.

Additionally, the image attached shows the graph of the given functions.

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What is the equation of the line that is parallel to the given
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Answer

O 4x+3y=-6

Step-by-step explanation:

Hello, I can help you witht this,

to solve this you need

step one

the line we are looking for is paraller to the line in the graph, it means both of then have the same slope.

find the slope of the line in the graph

remember

to find the slope of a line with two known points you can use

Let

P1(x_{1},y_{1})}\\P1(x_{2},y_{2})\\slope\\s=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

pick two points from he graph

P1(0,3)

P2(3,-1)

put the values into the equation

slope(m)\\m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{-1-3}{3-0}\\m=   \frac{-4}{3}

so, the slope of the line we are looking for is m=-4/3  and passes through the point (-3,2)

step 2

use the equation

y-y_{1}=m(x-x_{1})

to ding the equation of the line

P1(-3,2)

y-y_{1}=m(x-x_{1})\\y-2=\frac{-4}{3} (x+3})\\isolate\ y\\y-2=\frac{-4x}{3}-4\\y=\frac{-4x}{3}-4+2\\y+\frac{4x}{3}=-2\\multiply\ each\ side\ by\ 3\\3(y+\frac{4x}{3})=3*-2\\\\3y+4x=-6\\4x+3y=-6\\

and that's all, that is the equation of the line that is parallel to the given

line and passes through the point (-3, 2).

Have a good day.

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