Determine o período e o conjunto imagem, construindo o gráfico de um período completo para cada função dada. a) por f(x) = 1+ 4 sen x. b) por f(x) = 2sen (x-3)

The given functions are

The sine function has a standard period of 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 .

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

So, the function has an image defined by the set . 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 .

About the second function , the image set is , because the function was streched by a factor of 2.

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

did you get the answer yet?

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.