Transformations of Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

What is a transformation in the context of functions?

Back

A transformation is an operation that moves or changes a function's graph in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does it mean to reflect a graph across the x-axis?

Back

Reflecting a graph across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How do you represent a vertical shift of a function?

Back

A vertical shift is represented by adding or subtracting a constant from the function. For example, y = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

How do you represent a horizontal shift of a function?

Back

A horizontal shift is represented by adding or subtracting a constant inside the function's argument. For example, y = f(x - h) shifts the graph right by h units if h > 0 and left if h < 0.

Front

What is the effect of a negative sign in front of an absolute value function?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis.

Front

What is the equation of an absolute value function shifted right 3 units?

Back

y = |x - 3|.

Front

What is the equation of an absolute value function shifted down 4 units?

Back

y = |x| - 4.

Front

What does the notation (x - h)² represent in transformations?

Back

The notation (x - h)² represents a horizontal shift of the graph of the function to the right by h units.

Front

What does the notation (x + k)² represent in transformations?

Back

The notation (x + k)² represents a horizontal shift of the graph of the function to the left by k units.