The Absolute Value Function and Creating Equations for Sinusoidal Functions

Hey Guys It's Darian, I'm a little late, but better late then never.
Yesterday We learned about The Absolute Value Function and Other Absolute Value Graphs

This topic was all about absolute values and shifting rules and how they affect a graph.

So say we have a graph that is f (x)= |x| it will look like this

While a graph that is f (x)=x it will look like this

What im trying to get across is that when your dealing with absolute values any negative ooint will be positive Unless your dealing with a question that has a negative sign infront of the x like this

f (x)= -|x| which will turn out like this

We also learned about shifting functions, When a graph is shifted we read horizontal shifts (h values) as opposite of what is given and vertical shifts (k values) as is.


So say we have a question that is asking us to graph f (x) = |x - 3| + 4
You would graph this by first graphing a regular f (x) = |x| graph which looks like the one above, then you would shift it 3 points to the right and 4 points up which would result in the graph looking like this.

We also learned Creating Equations for Sinusoidal Function
f (x) =asinb (x-c)+d    Or      f(x) = acosb (x-c) + d

a - amplitude
                                                
b - affects the period - period= 2π/b

c - horizontal shift

d - vertical shift


Steps:
1. Identify the middle axis. This determines if there is any up or down shifting - the d value.
2.Find the amplitude - the a value.
3.Determine the period and then calculate the b value.
4.Identify the type of original wave - either    y=sin x or y= cos x.
5.Create the first equation including the a,b,c,and d values.
6.Create the second and third equations including the a,b,c,and d values.
7.Double check the horizontal shift symbols.
8.Double check the symbol of the a value in the equation.
Here are some Sinussoidal Functions

Now I know that this was kinda dull so to spice it up.....Heres a picture of a kitty

Hope you enjoyed :)