Question

Graph a sine function whose amplitude is 4, period is π , midline is y=−3 , and y-intercept is (0, −3) . The graph is not a reflection of the parent function over the x-axis.

Use the sine tool to graph the function.

The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Answer 1

Right so when you want to graph a sine function always start at the origin (unless its translated, in this case it went down 3 **Midline is -3 and y-intercept is 0,-3)

Start at (0,-3)

Now to know where you must put the maximum and minimum values you must know the period (which in this case is \(\pi\)

Half of π is \(\frac{π}{2}\) so that is where the graph reaches the origin again


Now to find the max and minimum x values find half between the distance of 0 and \(\frac{π}{2}\) [Which is \(\frac{π}{4}\)]

Amplitude tells you how far from the starting point it goes up/down, so the first max value is (\(\frac{π}{4},1\)), the first minimum value should be at y=-7

Between \(\frac{π}{2}\) and π, is the minimum, so add \(\frac{π}{4}\) to \(\frac{π}{2}\) [This is \(\frac{3π}{4}\)], this is your minimum value -- (\(\frac{3π}{4},-7\))

In the end you should get something like this
https://www.desmos.com/calculator/ivcjo8jyi3