Function Translations

Front

What is a translation in the context of functions?

Back

A transformation that moves a graph to a different location without changing its shape or orientation.

Front

What happens to the graph of f(x) when you add a positive number to it, like g(x) = f(x) + 4?

Back

The graph shifts up by 4 units.

Front

What happens to the graph of f(x) when you subtract a positive number from it, like g(x) = f(x) - 4?

Back

The graph shifts down by 4 units.

Front

If g(x) = f(x - 3), what type of transformation occurs?

Back

The graph shifts to the right by 3 units.

Front

If g(x) = f(x + 3), what type of transformation occurs?

Back

The graph shifts to the left by 3 units.

Front

What is the effect of multiplying a function by a positive constant, like g(x) = 2f(x)?

Back

The graph stretches vertically by a factor of 2.

Front

What is the effect of multiplying a function by a negative constant, like g(x) = -f(x)?

Back

The graph reflects over the x-axis.

Front

What does the transformation g(x) = f(x) + k represent?

Back

A vertical translation of the graph by k units.

Front

What does the transformation g(x) = f(x - h) represent?

Back

A horizontal translation of the graph to the right by h units.

Front

What is the parent function of a square root function?

Back

f(x) = √x.