Warm Up Wednesday

1. Given this table, what is the slope?

X Y1 45 12-3 -4

Given the equation:

2. Write an equation that is parallel to this equation?

3. Write an equation that is perpendicular to this equation?

4. Given the points (4, 3) and (2, 6) write an equation in point-slope form.

Transformations

Transformations in Nature

Transformations in Fiction

Transformations in Algebra

How do we Transform a Function?

Parent Function

Basically, parent functions are the function that you start a problem with before transforming it.

Translations

A Translation moves the parent function up/down or left/right.

Linear Transformations

If Kevin can buy a bag of popcorn at the theater for $4, what is his cost for 1, 2, 3 or more bags of popcorn?

f(x)

If Kevin has to buy a ticket for $6 before he can get in the theater, how much will it cost him for 1, 2, 3 or more bags of popcorn?

f(x)

Vertical Translations

If my parent function is f(x) = 4x and h(x) = f(x) + 6 what happens?

Take your original equation f(x) and replace it in your h(x) equation so that you get h(x) = 4x + 6

PracticeIf f(x) = 8x and h(x) = f(x) + 2 what is h(x)?

If g(t) = 12t and h(t) = g(t) - 9 what is h(t)?

h(x) = 8x + 2

h(t) = 12t - 9

Horizontal Translation

If my parent function is f(x) = 4x and h(x) = f(x + 6) what happens?

Take your original equation f(x) and replace x with (x + 6) so that you get h(x) = 4(x + 6) = 4x + 24.

PracticeIf f(x) = 8x and h(x) = f(x + 2) what is h(x)?

If g(t) = 12t and h(t) = g(t - 3) what is h(t)?

h(x) = 8(x+2) = 8x + 16

h(t) = 12(t – 3) = 12t - 36

Dilations

A dilation makes the function either bigger or smaller. If the number is greater than 1, the function grows, if it is between 0 and 1, the function shrinks.

Tiger = 2 Tiger

Vertical Dilation – Altering in the Y Direction

If my parent function is f(x) = and g(x) = 0.35f(x) what happens?

Take your original equation f(x) and replace it in your g(x) function so that you get g(x) = 0.35

PracticeIf f(x) = 8x and h(x) = 2 f(x) what is h(x)?

If g(t) = and h(t) = -2 g(t) what is h(t)?

If g(a) = 4a and f(a) = ½ (a) what is f(a)?

h(x) = 16x

h(t) =

f(a) = 2a

Horizontal Dilation – Altering in the X Direction

Take your original equation f(x) and replace the x with 2x so that you get

PracticeIf f(x) = 8x and h(x) = f(2x) what is h(x)?

If g(t) = and h(t) = g(-2t) what is h(t)?

If g(a) = 4a and f(a) = (a) what is f(y)?

h(x) = 8 = 16x

h(t) =

f(y) = 4 (a) = 2a

If my parent function is f(x) = and g(x) = f(2x) what happens?

Summary