September 18, 2015

September 18, 2015

September 18, 2015

September 18, 2015

September 18, 2015

September 18, 2015

September 18, 2015

(1.6) Graphical Transformations

Objective: Learn about transformations of functions and their effect on equations.

Why: To make connections about the relationships between graphs and their equations.

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

Two types of transformations:

Rigid: preserves congruence of figures (reflections, translations, rotations)

Nonrigid: generally distorts the shape (horizontal and vertical stretches and compressions)

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

1. Graph y = √xThen graph the following and describe how the graph transformed.:

a. y = √x + 4 ___________

b. y = √x - 4 ___________

c. y = √(x+4) ___________

d. y = √(x-4) ___________

What happens to a function: y = f(x) when:

a. y = f(x) + c ___________________

b. y = f(x) - c ___________________

c. y = f(x + c) ___________________

d. y = f(x - c) ___________________

Translations:

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

The figure shows a graph of y = x 3. Write an equation for y 2 and y 3.

y = x 3

y 2 = y 3 =

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

Graph y = √x Then graph the following and describe how the graph transformed.:

a. y = - √x _____________

b. y = √(-x) ____________

What happens to a function y = f(x) when:

a. y = - f(x) ___________________

b. y = f(-x) ____________________

Reflections:

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

Graph y = √(4-x2) Then graph the following and describe how the graph transformed.:

a. y = 2√(4-x2) _____________

b. y = 0.5√(4-x2) ___________

What happens to a function y = f(x) when y = c f(x) if:

a. c > 1 _______________________

b. 0 < c < 1 _____________________

Vertical Stretch/Compression:

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

Graph y = √(4-x2) Then graph the following and describe how the graph transformed.:

a. y = √(4-(2x)2) ____________

b. y = √(4-(0.5x)2) ___________

What happens to a function y = f(x) when y = f(cx) if:

a. c > 1: _________________________

b. 0 < c < 1: _______________________

Horizontal Stretch/Compression:

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

Graphing Absolute Value Compositions

Given the graph of y = f(x),

y = f(x) reflect the portion of the graph below the x-axis across the x-axis, leaving the portion above the x-axis unchanged.

y = f( x ) replace the portion of the graph to the left of the y-axis by a reflection of the portion to the right of the y-axis across the y-axis, leaving the portion to the right of the y- axis unchanged. (The result will show even symmetry)

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

The graph of y = x 2 undergoes the following transformations, in order. Find the equation of the graph that results.

* a horizontal shift 2 units to the right* a vertical stretch by a factor of 3* a vertical translation 5 units up

Combining Transformation in Order

September 18, 2015

Obj: Learn about transformations of functions and their effect on equations.

HW:

(HR): (1.6)Pg.136: 1-19odd, 23-29odd, 43, 49, 53