Chapter 6 by Jess Henry

Odd functions are symmetrical around the origin.

2018-02-02 16:42:37 UTC

inside changes are horizontal shifts

sgloe — 2018-02-02 16:42:49 UTC

Flipping over the axis

mdungan — 2018-02-02 16:43:00 UTC

y=-f(x) = flip over the x-axis
y=f(-x) = flip over the y-axis

Even functions reflect over the y axis

jfoster45 — 2018-02-02 16:43:27 UTC

Adding outside of the parenthesis moves the function vertically

jfoster45 — 2018-02-02 16:44:07 UTC

flipping over the X and Y axis

2018-02-02 16:44:23 UTC

odd functions are symmetric over origin and even functions are symmetric over the y axis

2018-02-02 16:44:28 UTC

2018-02-02 16:46:39 UTC

Even flip over Y
Odd 180 degree rotation

A function can have a horizontal and vertical shift

2018-02-02 16:48:23 UTC

reflections are transformation that flip a graph in the x-y pane without changing its shape

gjohnson43 — 2018-02-02 16:49:27 UTC

Odd Functions:

afreda1 — 2018-02-02 17:49:07 UTC

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)

sgloe — 2018-02-08 16:57:40 UTC

stretching or compressing a function changes the average rate of change, but not where the function is increasing or decreasing.

Steps for transformations

mdungan — 2018-02-08 17:01:10 UTC

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)

2018-02-08 17:01:17 UTC

When combining the transformations, follow P.E.M.D.A.S. It is the order in which the transformations are made

Equation

bswainprice — 2018-02-08 17:02:14 UTC

y=Af(B(X-h))+k

Does stretching or compressing a function change the average rate of change of a function?

2018-02-08 17:02:35 UTC

The average rate of change is altered by the vertical compression and stretch.

Horizontal Stretches/Compression

rmohammed1 — 2018-02-08 17:02:52 UTC

Horizontally Compressed: by factor of 1/k, k>1 and Horizontally Stretched by factor of 1/k, 0

Reflection

bswainprice — 2018-02-08 17:03:23 UTC

A<0 reflection about the x-axis,
B<0 reflection about the y-axis

Horizontal Stretch

2018-02-08 17:04:01 UTC

By a factor of 1/k if 0

horizontal shifts

2018-02-08 17:04:03 UTC

gjohnson43 — 2018-02-08 17:04:10 UTC

If f is a function and k is constant, then the graph of y= f(kx) is the

Function

2018-02-08 17:06:05 UTC

The graph y=f(kx) is equal to y=f(x)

If there has been a vertical stretch/compression, how do you find the new average rate of change?

afreda1 — 2018-02-08 17:06:49 UTC

If G(x)= K* f(x), then on any interval,
The average rate of G= K * (Avg. Rate of Change of F)

2018-02-08 17:06:50 UTC

the average rate of change of g= k x average rate of change for f.
g(x)- k x f(x)

New average rate of change is found by

cwaller4 — 2018-02-08 17:07:00 UTC

multiplying a * old slope

jfoster45 — 2018-02-08 17:07:31 UTC

Follow pemdas order of operations to manipulate the function.