are said to be if and only if and At the same time.

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Presentation transcript:

are said to be if and only if and At the same time

TEST and

are said to be if and only if and At the same time

are said to be if and only if THEY ARE INVERSE FUNCTIONS and

FOLD

y = x

(2, 0) FOLD OVER THE LINE

(2, 0) (0, 2)

(2, 0) (0, 2) (0,– 4) FOLD OVER THE LINE

(2, 0) (0, 2) (0,– 4) (– 4, 0)

(2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) FOLD OVER THE LINE

(2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6)

(2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) The x’s and y’s traded places

(2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) The x’s and y’s traded places

(2, 0) (0, 2) (0,– 4) (– 4, 0) (6, 8) (8, 6) These points are called the INVERSES

Inverse Functions Are Reflections over the Line y = x

Given the relation: FIRST IT MUST BE A

Given the relation:

It must be

Independent Variable Abscissa Dependent Variable Ordinate xy

xy Independent Variable Abscissa Dependent Variable Ordinate The Dependent and Independent Variables Trade Places INVERSE FUNCTION

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate 1 INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate -51 INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION Independent Variable Abscissa Dependent Variable Ordinate xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Independent Variable Abscissa Dependent Variable Ordinate Independent Variable Abscissa Dependent Variable Ordinate INVERSE FUNCTION xy

Is it a FUNCTION? Is it a ONE-TO-ONE?

INVERSE FUNCTION

Find The Equation of the Line

y = 2 x – 4

Find The Equation of the Line y = 2x – 4

y = ½ x + 2

INVERSE FUNCTION

Any Vertical Line Drawn Intersects The Graph No More Than Once

Any Horizontal Line Drawn Intersects The Graph No More Than Once

INVERSE FUNCTION

Independent Variable Abscissa Dependent Variable Ordinate

The Dependent and Independent Variables trade places

Solve For The New y

INVERSE FUNCTION

FUNCTION

Match y = 2x – 4 y = ½ x + 2

The Dependent and Independent Variables trade places

INVERSE FUNCTION FUNCTION

The Dependent and Independent Variables trade places

INVERSE FUNCTION FUNCTION

()

The Dependent and Independent Variables trade places

INVERSE FUNCTION FUNCTION

() () When you put in into the Calculator

The Dependent and Independent Variables trade places

INVERSE FUNCTION FUNCTION