FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both)...

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FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function at origin. Function translated horizontally. (x + h) is h units left and (x – h) is h units right because horizontal changes are inversed. f(x) = (x) + k Function translated vertically. (x) + k is k units up. (x) – k is k units down. f(x) = (x + h) f(x) = (x) – k

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FUNCTION TRANSLATIONS ADV151 g(x) =  x – 2  + 7 h(x) = – 5 1 x – 3 f(x) = (x + 5) 2 – 4 g(x) = Describe the translation of each function. Answers on next slide.

Transcript of FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both)...

Page 1: FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

FUNCTION TRANSLATIONSADV151

TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph.

f(x) = x

f(x) = (x – h)

Parent function at origin.

Function translated horizontally. (x + h) is h units left and (x – h) is h units right because horizontal changes are inversed.

f(x) = (x) + k Function translated vertically. (x) + k is k units up. (x) – k is k units down.

f(x) = (x + h)

f(x) = (x) – k

Page 2: FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

FUNCTION TRANSLATIONSADV151

g(x) = (x – 2) + 6The 2 is a horizontal shift right and the 6 is a vertical shift up. Basically you add 2 to every x-coordinate and add 6 to every y-coordinate.

g(x) = (x + 4)The +4 is grouped with the x so it’s a horizontal translation. Basically you subtract 4 from every x-coordinate.

g(x) = (x) + 3The +3 is NOT grouped with the x so it’s a vertical translation. Basically you add 3 to every y-coordinate.

Page 3: FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

FUNCTION TRANSLATIONSADV151

g(x) = x – 2 + 7

h(x) = – 51x – 3

f(x) = (x + 5)2 – 4

41x g(x) =

Describe the translation of each function.

Answers on next slide.

Page 4: FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

FUNCTION TRANSLATIONSADV151

g(x) = x – 2 + 7

h(x) = – 5 1x – 3

f(x) = (x + 5)2 – 4

41x g(x) =

Describe the translation of each function.ANSWERS!

2 units right7 units up

5 units left4 units down

1 units right4 units up

3 units right5 units down


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