Translations of Linear Functions

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Presentation transcript:

Translations of Linear Functions Define the two terms in your own words with regards to math: Translation Linear Function

Answers Define the two terms in your own words: Translation – a slide of a figure where every point is moved the same direction and same distance Linear Function – any function that graphs to a straight line

An example of four linear functions translated to a new position.

Translations of Linear Functions COMMON CORE #8, #31a, #36 Basically, exploring the change from y = x to y = m(x – h) + k IT WILL NOT BE EASY GET YOUR GAME FACE ON!!!!!!!!!!!!!!

Translations of Linear Functions Graph y = 2x Translate the graph 4 units to the right by moving each point you plotted. Write the equation of the translated line. y = 2x - 8

Translations of Linear Functions y = 2x – 8 (4) Factor the expression: y = 2(x – 4) (5) What are the coordinates of the translated point (0, 0) (4, 0)

Translations of Linear Functions y = 2x (0, 0) y = 2(x – 4) (4, 0) (6) Where does the amount of the translation appear in the factored form of the equation? -4 which moves it right 4 units

Translations of Linear Functions y = mx + b y = 2x y = m(x – h) + k y = 2(x – 4) + k What about k? It is 0 in this case as we did not move up or down(y- axis)

Translations of Linear Functions (7) Graph y = 2x (8) Translate the graph 4 units to the left by moving each point you plotted. (9) Write the equation of the translated line. y = 2x + 8

Translations of Linear Functions y = 2x + 8 (10) Factor the expression: y = 2(x + 4) (11) What are the coordinates of the translated point (0, 0) (-4, 0)

Translations of Linear Functions y = 2x (0, 0) y = 2(x + 4) (-4, 0) (12) Where does the amount of the translation appear in the factored form of the equation? +4 which moves it left 4 units

Translations of Linear Functions y = mx + b y = 2x y = m(x – h) + k y = 2(x – (-4)) + k y = 2(x + 4) + k What about k? It is 0 in this case as we did not move up or down(y- axis)

Translations of Linear Functions YOUR TURN TO TRY GRAPH y = 3(x – 2)

Translations of Linear Functions YOUR TURN TO TRY GRAPH y = 4(x + 2)