Class Opener:

Find the difference quotient and simplify your answer:

Review: Even & Odd FunctionsDetermine whether each function is even, odd, or neither.

Vertical and Horizontal Shifts

How can you shift the graph of up two units?

How can you shift a the same parent function graph two units to the right?

Vertical and Horizontal Shifts

Let c be a positive real number. Vertical and Horizontal Shifts in the graph of y = f(x) are represented as follows.

1. Vertical shift c upward: h(x) = f(x) + c 2. Vertical shift c downward: h(x) = f(x)-c3. Horizontal shift c units to the right:

h(x) = f(x-c)4. Horizontal shift c units to the left: h(x)

= f(x+c)

Shifts in graphs of functions:

Compare the graph of each function with the graph of

Student Check:

How do the graphs of the following functions compare with one another:

Writing Equations of Graphs

Turn to Page 49

Problems 15 – 18

Reflecting Graphs

Reflections in the coordinate axes of the graph of y = f(x) are represented by:

1. Reflection in the x-axis: h(x) = -f(x)2. Reflection in the y-axis: h(x) = f(-x)

Reflecting graphs

Use a graphing utility to graph the three functions in the same viewing window. Describe the graphs of g and h relative the graph of f.

Reflections and Shifts

Compare the graph of each function with the graph of f(x) = alegebraically

Non-rigid Transformations

Horizontal, vertical, and reflection shifts are all call rigid transformations. These transformations only change the position of the graph in the coordinate plane

Non-rigid transformations are those that cause distortion of the graph.

Non-rigid Vertical Stretch & Shrink

A non-rigid transformation of the graph y= f(x) is represented by y = cf(x), where the transformation is a vertical stretch if c > 1 and a vertical shrink if 0 < c< 1.

Non-rigid Horizontal Stretch & Shrink

Another non-rigid transformation of the graph y = f(x) is represented by h(x) = f(cx), where the transformation is a horizontal shrink if c > 1 and a horizontal stretch if 0<c<1

Compare the Graphs

Write a few sentences comparing the graphs shown above.

Assignment:

Pg. 48 -50#9-12, 14-20, 22-42 even, 53-74