# How do you graph  y= -3/4 sin ( pi/5 x) - 7/4?

Mar 13, 2018

In the description...

#### Explanation:

As we know a sinusoidal graph is basically of periodic nature with a certain amplitude and a period.
It doesn't matter if amplitude is negative.
So $| \left(P\right) | = | - \frac{3}{4} | = \frac{3}{4}$
Hence the graph will hit it's maximum at $x + \frac{3}{4}$ and $x - \frac{3}{4}$
Get the period by:
$2 \frac{\pi}{\pi} / 5$=$10$
The vertical transformation given is $x = - \frac{7}{4}$
So maximum points are $- \frac{7}{4} + \frac{3}{4}$ and $- \frac{7}{4} - \frac{3}{4}$
The pattern a sine wave is drawn is
Intercept-Max-Int-Min-Intercept
So, points are $\left(0 , - \frac{7}{4}\right)$
$\left(2.5 , - \frac{7}{4} + \frac{3}{4}\right)$ $\left(5 , - \frac{7}{4}\right)$ $\left(7.5 , - \frac{7}{4} - \frac{3}{4}\right)$ and $\left(10 , - \frac{7}{4}\right)$
Note that I divided the interval into $\frac{1}{4}$ pieces so that each piece of left end point of interval will correspond to the pattern of graph. Now graph the function with an odd symmetry.