# data[].attributes.body
y=-f(x) = flip over the x-axis
y=f(-x) = flip over the y-axis

# data[].attributes.headline
Odd functions are symmetrical around the origin.

# data[].attributes.subject
Odd functions are symmetrical around the origin.

# data[].attributes.headline
Adding outside of the parenthesis moves the function vertically 

# data[].attributes.subject
Adding outside of the parenthesis moves the function vertically 

# data[].attributes.headline
odd functions are symmetric over origin and even functions are symmetric over the y axis

# data[].attributes.subject
odd functions are symmetric over origin and even functions are symmetric over the y axis

# data[].attributes.body
Even flip over Y
Odd 180 degree rotation

# data[].attributes.headline
A function can have a horizontal and vertical shift 

# data[].attributes.subject
A function can have a horizontal and vertical shift 

# data[].attributes.headline
reflections are transformation that flip a graph in the x-y pane without changing its shape

# data[].attributes.subject
reflections are transformation that flip a graph in the x-y pane without changing its shape

# data[].attributes.body
You know that this is an odd function because it goes through the origin. If you rotate the graph 180 degrees about the origin it will map onto itself.  (look at the picture)

# data[].attributes.body
stretching or compressing a function changes the average rate of change, but not where the function is increasing or decreasing.

# data[].attributes.body
Step 1 = horizontal shift (left or right)
Step 2 = Vertical Compression
Step 3 = Vertical reflection across the x-axis
Step 4= = Vertical shift (up or down)

# data[].attributes.body
When combining the transformations, follow P.E.M.D.A.S. It is the order in which the transformations are made

# data[].attributes.body
y=Af(B(X-h))+k

# data[].attributes.headline
Does stretching or compressing a function change the average rate of change of a function?

# data[].attributes.subject
Does stretching or compressing a function change the average rate of change of a function?

# data[].attributes.body
The average rate of change is altered by the vertical compression and stretch.

# data[].attributes.body
Horizontally Compressed: by factor of 1/k, k>1 and Horizontally Stretched by factor of 1/k, 0<k<1

# data[].attributes.body
A<0 reflection about the x-axis,
B<0 reflection about the y-axis

# data[].attributes.body
If f is a function and k is constant, then the graph of y= f(kx) is the

# data[].attributes.body
By a factor of 1/k if 0<k<1

# data[].attributes.body
The graph y=f(kx) is equal to y=f(x)

# data[].attributes.body
the average rate of change of g= k x average rate of change for f.
g(x)- k x f(x)

# data[].attributes.body
multiplying a * old slope

# data[].attributes.headline
If there has been a vertical stretch/compression, how do you find the new average rate of change?

# data[].attributes.subject
If there has been a vertical stretch/compression, how do you find the new average rate of change?

# data[].attributes.body
If G(x)= K* f(x), then on any interval,
The average rate of G= K * (Avg. Rate of Change of F)

# data[].attributes.body
Follow pemdas order of operations to manipulate the function.