Transformations of Functions

Front

What is a translation in the context of function transformations?

Back

A translation is a transformation that shifts a graph horizontally, vertically, or both without changing its shape.

Front

If a point (x, y) is translated 5 units left and 6 units up, what are the new coordinates?

Back

The new coordinates are (x - 5, y + 6).

Front

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

Back

It represents a reflection of the function f(x) over the x-axis.

Front

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

Back

It represents a reflection of the function f(x) over the y-axis.

Front

What is the effect of shifting a graph up by c units?

Back

The new function will be f(x) + c.

Front

What is the effect of shifting a graph down by c units?

Back

The new function will be f(x) - c.

Front

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

Back

It indicates that the graph of g(x) is reflected over the x-axis.

Front

What does the transformation y = g(x + c) indicate?

Back

It indicates a horizontal shift of the graph of g(x) to the left by c units.

Front

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

Back

It indicates a horizontal shift of the graph of g(x) to the right by c units.

Front

If f(x) = x^2, what is the transformation for f(x) = (x + 3)^2?

Back

The graph of f(x) is shifted left 3 units.