parent functions and transformations

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 in the function y = (x - 3)²?

Back

The graph is translated right by 3 units.

Front

How does the function y = f(x - 4) transform the parent function?

Back

It shifts the graph right by 4 units.

Front

What type of function is represented by y = √x?

Back

Square root function.

Front

What is the effect of adding a constant outside the function, such as in y = x² + 5?

Back

It translates the graph vertically up by 5 units.

Front

What transformation does the function y = -(x + 2)² represent?

Back

It reflects the graph over the x-axis and translates it left by 2 units.

Front

What is the general form of a quadratic function?

Back

The general form is y = ax² + bx + c, where a, b, and c are constants.

Front

How does the function y = (x - 2)² - 1 transform the parent function y = x²?

Back

It translates the graph right by 2 units and down by 1 unit.

Front

What is a vertical stretch in the context of transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1.

Front

What does the function y = (1/2)x² represent in terms of transformations?

Back

It represents a vertical compression of the parent function y = x².