Transformations of Functions Review

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean to shift a graph to the right?

Back

Shifting a graph to the right means adding a positive value to the x-variable in the function's equation.

Front

What does it mean to shift a graph up?

Back

Shifting a graph up means adding a positive value to the entire function, which raises the graph vertically.

Front

What is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

How does reflecting a graph over the x-axis affect its equation?

Back

Reflecting a graph over the x-axis changes the sign of the function, resulting in f(x) becoming -f(x).

Front

What is the effect of the transformation y = f(x) - k?

Back

The transformation y = f(x) - k shifts the graph of f(x) down by k units.

Front

What is the effect of the transformation y = f(x + h)?

Back

The transformation y = f(x + h) shifts the graph of f(x) to the left by h units if h is positive.

Front

What does the equation y = -x² + 2 represent?

Back

The equation y = -x² + 2 represents a quadratic function that is reflected over the x-axis and shifted up 2 units.

Front

How do you identify a vertical shift in a function?

Back

A vertical shift can be identified by the constant added or subtracted from the function, such as in y = f(x) + c.

Front

What does the transformation y = f(x - 3) do to the graph?

Back

The transformation y = f(x - 3) shifts the graph of f(x) to the right by 3 units.