contestada

A sinusoidal function whose period is 1/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3.

What is the equation of the function described?




f(x)=7cos(4x)+3

f(x)=7sin(4πx)+3

f(x)=7cos(4πx)+3

f(x)=7sin(4x)+3

Respuesta :

Ans: f(x)=7sin(4pix) + 3

We see the period, which is equivalent to 2pi divided by the coefficient of the argument of the trigonometric function, is 1/2 since 2pi/4i = 1/2

We see the maximum value of f(x) is 10 since sin(x) is bounded such that         -1 < sin(x) < 1, therefore -7 < 7sin(x) < 7. And since we are adding 3 at the end of the equation, we can say the graph of 7sin(x) is shifted vertically 3 units, thus we have a max value of 10 and min value of -4 ( -4 < 7sin(x) + 3 < 10) 

The y-intercept is seen as 3 since the sine function, at 0 radians i.e. x=0, has a value of 0 at the origin, this from the +3, we see the y-value of f(x) at the origin is 3. 
facundo3141592

The sinusoidal function that meets all the conditions is:

f(x)=7sin(4πx)+3

What is the equation of the function described?

The difference between the maximum and the minimum, over two, gives the amplitude:

A = (10 - (-4))/2 = 7

The y-intercept is the value of the function when we evaluate in x = 0. As you can see, all the options have a midline of 3. So we need to select the sine options, because we know that sin(0) = 0.

So the remaining options are:

f(x)=7sin(4πx)+3

f(x)=7sin(4x)+3

Now notice that the period is 1/2, while the period of the sinusoidal functions depends on pi. Then we need to have a form of pi in the argument of the sine function.

Only with that, we conclude that the correct option is:

f(x)=7sin(4πx)+3

Where is evident that the period T is equal to 1/2, because:

4π(x + 1/2) = 4πx + 2π

And 2π is the natural period of the sine function.

If you want to learn more about sine functions:

https://brainly.com/question/9565966

#SPJ5

Otras preguntas