Function Transformations

Front

What is a vertical shift in function transformations?

Back

A vertical shift occurs when a function is moved up or down on the graph. For example, h(x) = f(x) + k shifts the graph of f(x) up by k units if k > 0 and down by k units if k < 0.

Front

What does the equation h(x) = f(x) + 2 represent?

Back

The equation represents a vertical shift of the function f(x) upwards by 2 units.

Front

What is a horizontal shift in function transformations?

Back

A horizontal shift occurs when a function is moved left or right on the graph. For example, g(x) = f(x - h) shifts the graph of f(x) to the right by h units if h > 0 and to the left by h units if h < 0.

Front

What does the equation p(x) = f(x + 3) represent?

Back

The equation represents a horizontal shift of the function f(x) to the left by 3 units.

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch occurs when the output of a function is multiplied by a factor greater than 1, making the graph taller. For example, s(x) = kf(x) where k > 1.

Front

What does the equation s(x) = 7f(x) indicate?

Back

The equation indicates a vertical stretch of the function f(x) by a factor of 7.

Front

What is a vertical compression in function transformations?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does the equation g(x) = f(x) - 5 represent?

Back

The equation represents a vertical shift of the function f(x) downwards by 5 units.

Front

What is the effect of the transformation g(x) = f(x + 5)?

Back

The transformation shifts the graph of f(x) to the left by 5 units.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.