Question

Find the domain and range of

f(x) = 2sinπx
please help me!
how do I graph this function​

Answer 1

Explanation:

The general form of a sine wave is:

y = A sin(2π/T x − B) + C

where A is the amplitude,

T is the period,

B is the phase (horizontal shift),

and C is the midline (vertical shift).

f(x) = 2 sin(πx)

This is a sine wave with an amplitude of 2, a period of 2, a phase of 0, and a midline of y=0.

To graph, the wave is centered at y=0 and has zeros every half period (x = 0, 1, 2, 3, etc.). Between the zeros, the wave is either a min or max (±2).

The domain of the function is (-∞, ∞).

The range of the function is [-2, 2].

Answer 2

For

`f(x) = 2\sin(\pi x)`

the domain is the real numbers, Range = [-2,2]

Explanation:

About the domain, you can take any number, remember that the domain are the "x" that you can plug in on your function, for this case, you can plug in any value and you will have no problem.

Think about it like this, if you have f(x)= 1/x , you can't plug in x=0, but you can plug in all the other numbers, so the domain of that function would be all numbers except 0.

Therefore for

`f(x) = 2\sin(\pi x)`

the domain is the real numbers.

About the range, it is the "y" axis, which numbers can you reach on the "y" axis, if you graph the function you will see that it is between [-2,2]

Range = [-2,2]

check the image I attach.