Transformations of Parent Functions

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for creating more complex functions through transformations.

Front

What transformation occurs when a function is reflected over the x-axis?

Back

The output values of the function are multiplied by -1, resulting in a vertical flip of the graph.

Front

How does shifting a function up affect its equation?

Back

To shift a function up by 'k' units, add 'k' to the output of the function: f(x) becomes f(x) + k.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph taller.

Front

What does a vertical shrink do to a function's graph?

Back

A vertical shrink multiplies the output of the function by a factor between 0 and 1, making the graph shorter.

Front

How do you represent a horizontal shift to the left in a function's equation?

Back

To shift a function left by 'h' units, replace 'x' with 'x + h' in the function's equation.

Front

What is the transformation for the equation g(x) = -x^2 + 2?

Back

This represents a reflection over the x-axis and a vertical shift up 2 units from the parent function f(x) = x^2.

Front

What does the equation y = |x - 5| represent in terms of transformations?

Back

This represents an absolute value function shifted right 5 units from the parent function y = |x|.

Front

What is the transformation for the equation g(x) = 5x^2 + 2?

Back

This represents a vertical stretch by a factor of 5 and a vertical shift up 2 units from the parent function f(x) = x^2.

Front

How do you translate a quadratic function left by 4 units?

Back

To translate left by 4 units, the equation becomes y = (x + 4)^2.