Function Transformations

Front

What is a transformation in the context of functions?

Back

A transformation refers to the alteration of a function's graph through shifts, stretches, compressions, or reflections.

Front

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

Back

A horizontal shift to the left by c units.

Front

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

Back

A horizontal shift to the right by c units.

Front

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

Back

A vertical shift upward by k units.

Front

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

Back

A vertical shift downward by k units.

Front

What is the effect of a negative sign in front of the function, such as g(x) = -f(x)?

Back

It reflects the graph of the function across the x-axis.

Front

What is the effect of a vertical stretch in a function?

Back

It increases the distance of points from the x-axis, making the graph taller.

Front

What is the effect of a vertical compression in a function?

Back

It decreases the distance of points from the x-axis, making the graph shorter.

Front

What does the transformation g(x) = af(x) do when |a| > 1?

Back

It stretches the graph vertically.

Front

What does the transformation g(x) = af(x) do when 0 < |a| < 1?

Back

It compresses the graph vertically.