Translations of Functions Flashcard

Front

What is the equation for the translation of f(x)=|x| that moves up 6 units?

Back

f(x) = |x| + 6

Front

What is the equation for the translation of f(x)=|x| that moves left 8 units and up 3 units?

Back

f(x) = |x + 8| + 3

Front

What shifts have occurred in the translation of a function that moves right 1 unit and up 5 units?

Back

right 1, up 5

Front

What is the equation for the translation of f(x)=|x| that moves down 3 units and right 5 units?

Back

f(x) = |x - 5| - 3

Front

Describe the transformations of the graph y = (x - 3)² - 2.

Back

Right 3, Down 2

Front

What is the general form of a vertical translation of a function f(x)?

Back

f(x) + k, where k is the number of units moved up (k > 0) or down (k < 0).

Front

What is the general form of a horizontal translation of a function f(x)?

Back

f(x - h), where h is the number of units moved right (h > 0) or left (h < 0).

Front

If f(x) = |x|, what is the effect of adding a positive constant to the function?

Back

It translates the graph upward by that constant value.

Front

If f(x) = |x|, what is the effect of subtracting a positive constant from the function?

Back

It translates the graph downward by that constant value.

Front

What is the effect of replacing x with (x + h) in the function f(x)?

Back

It translates the graph left by h units if h > 0 and right by h units if h < 0.