Parent Function Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear, quadratic, cubic, absolute value, and exponential functions.

Front

What is the effect of a positive constant added to a function?

Back

Adding a positive constant to a function translates the graph upward by that constant value.

Front

What is the effect of a negative constant added to a function?

Back

Adding a negative constant to a function translates the graph downward by that constant value.

Front

What does it mean to translate a function left or right?

Back

Translating a function left or right involves shifting the graph horizontally. A positive value shifts it left, while a negative value shifts it right.

Front

Back

The function is translated right 3 units.

Front

Back

The function is translated up 5 units.

Front

What does a vertical stretch of a function do?

Back

A vertical stretch multiplies the function's output by a factor greater than 1, making the graph steeper.

Front

What does a vertical compression of a function do?

Back

A vertical compression multiplies the function's output by a factor between 0 and 1, making the graph flatter.

Front

What is the effect of a negative coefficient in front of a function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

Back

The function is reflected across the x-axis, stretched vertically by a factor of 2, translated left 1 unit, and translated up 3 units.