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

Back

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

Front

What does it mean to compress a function vertically by a factor of 1/2?

Back

The y-values of the function are halved, making the graph closer to the x-axis.

Front

What is the effect of shifting a graph to the left by 1 unit?

Back

Every point on the graph moves 1 unit to the left, changing the x-values of the function.

Front

How does a vertical shift of 3 units down affect a function?

Back

Every point on the graph moves down 3 units, decreasing the y-values of the function by 3.

Front

What is the equation of a quadratic function that opens downwards?

Back

The general form is y = -ax^2 + bx + c, where a > 0.

Front

What transformation is represented by the equation y = (x - 2)^2 + 4?

Back

This represents a right shift of 2 units and an upward shift of 4 units from the parent function y = x^2.

Front

What does it mean to reflect a graph over the y-axis?

Back

The x-values of the function are replaced with their opposites, resulting in a horizontal flip of the graph.

Front

What is the parent function of a square root function?

Back

The parent function is y = √x.

Front

How do you identify a quadratic function from its equation?

Back

A quadratic function has the form y = ax^2 + bx + c, where a ≠ 0.