Asinusoidal 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

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.