Translating Functions

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What transformation occurs when f(x) is changed to f(x+3)?

Back

Translation left 3 units.

Front

Which equation represents an absolute value graph shifted right 5 units?

Back

y = |x - 5|.

Front

Identify the transformation: g(x) = f(x) - 7.

Back

Translated 7 units down.

Front

Which equation represents a quadratic function shifted down 4 units?

Back

y = x^2 - 4.

Front

What is a translation in the context of functions?

Back

A translation is a shift of a graph in the coordinate plane without changing its shape.

Front

How does adding a positive number to f(x) affect the graph?

Back

It translates the graph up by that number of units.

Front

How does subtracting a positive number from f(x) affect the graph?

Back

It translates the graph down by that number of units.

Front

What effect does changing f(x) to f(x - k) have on the graph?

Back

It translates the graph right by k units.

Front

What effect does changing f(x) to f(x + k) have on the graph?

Back

It translates the graph left by k units.