Transformation of Functions

Front

What is the vertex of the quadratic function f(x) = a(x - h)² + k?

Back

The vertex is the point (h, k).

Front

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

Back

A horizontal shift to the left by c units.

Front

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

Back

A horizontal shift to the right by c units.

Front

What transformation does g(x) = af(x) represent when a > 1?

Back

A vertical stretch by a factor of a.

Front

What transformation does g(x) = af(x) represent when 0 < a < 1?

Back

A vertical shrink by a factor of a.

Front

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

Back

A vertical shift upward by k units.

Front

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

Back

A vertical shift downward by k units.

Front

If f(x) = (x - 3)² + 5, what are the transformations from the parent function y = x²?

Back

Right 3 and up 5.

Front

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

Back

A reflection over the x-axis.

Front

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

Back

A reflection over the y-axis.