Function Transformations

Front

What is a vertical stretch in function transformations?

Back

A vertical stretch occurs when a function is multiplied by a scale factor greater than 1, making the graph taller.

Front

What is a vertical compression in function transformations?

Back

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

Front

How does reflecting a function over the y-axis affect its equation?

Back

Reflecting a function over the y-axis changes the equation from f(x) to f(-x).

Front

What does shifting a function down by 'k' units look like in its equation?

Back

Shifting a function down by 'k' units is represented as g(x) = f(x) - k.

Front

What does shifting a function left by 'h' units look like in its equation?

Back

Shifting a function left by 'h' units is represented as g(x) = f(x + h).

Front

What does reflecting a function over the x-axis do to its equation?

Back

Reflecting a function over the x-axis changes the equation from f(x) to -f(x).

Front

What is the effect of a horizontal shift on the graph of a function?

Back

A horizontal shift moves the graph left or right without changing its shape.

Front

What is the transformation represented by g(x) = f(x + 3)?

Back

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

Front

What is the transformation represented by g(x) = -f(x)?

Back

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

Front

What does the transformation g(x) = 5f(-x) - 4 indicate?

Back

This transformation indicates a reflection over the y-axis, a vertical stretch by a factor of 5, and a downward shift of 4 units.