could somebody please help me with my transformations.
y = 0.5sin(x/4 - x/16) -5
I might be dooing it wrong but i rearanged it to
y = 0.5sin(x - x/4) -5
is this correct?
in any case, what would be the period and x translation?
could somebody please help me with my transformations.
y = 0.5sin(x/4 - x/16) -5
I might be dooing it wrong but i rearanged it to
y = 0.5sin(x - x/4) -5
is this correct?
in any case, what would be the period and x translation?
$\displaystyle y = A\sin(Bx+C) + D$
A is the amplitude - this is how "high" the graph will go relative to$\displaystyle \pm 1$. For example if A = 2 the extrema will be $\displaystyle \pm 2$
B affects the period of the graph. For $\displaystyle B>1$ the graph will have a shorter period and for $\displaystyle B<1$ a longer period. On a graph this means that the wave will be more or less "squashed" on the x axis respectively.
C is the phase difference which determines the shift on the x axis of the graph. The shape doesn't change, just it's positions and intercepts. For $\displaystyle C>0$ the graph will move to the left and for $\displaystyle C<0$ to the right. $\displaystyle C=0$ is no change obviously enough
D is the y-shift. In other words how much the whole graph is shifted either up or down the y axis.
In your case you have
- $\displaystyle A = 0.5$
- $\displaystyle B = 13/16$
- $\displaystyle C = 0$
- $\displaystyle D = -5$
I have plotted the graphs of $\displaystyle y = 0.5\sin(13x/16)$ in orange, $\displaystyle y = \sin(13x/16)$ in green and $\displaystyle y = \sin(x)$ in blue for comparison purposes
$\displaystyle y = 0.5\sin(13x/16) - 5$ is on a separate attachment