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 does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally, vertically, or both without changing its shape.

Front

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

Back

Adding a positive value to a function shifts its graph upward.

Front

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

Back

Adding a negative value to a function shifts its graph downward.

Front

How does a transformation of 'left 2' affect the function f(x)?

Back

A transformation of 'left 2' shifts the graph of the function 2 units to the left.

Front

How does a transformation of 'right 2' affect the function f(x)?

Back

A transformation of 'right 2' shifts the graph of the function 2 units to the right.

Front

What is the transformation for f(x) = (x - 3)^2?

Back

The transformation shifts the parent function y = x^2 to the right by 3 units.

Front

What is the transformation for f(x) = x^2 + 4?

Back

The transformation shifts the parent function y = x^2 upward by 4 units.

Front

What does the notation f(x) = |x| - 5 represent?

Back

This represents a vertical shift of the absolute value function down by 5 units.

Front

Which equation represents a quadratic function translated left 4 units?

Back

y = (x + 4)^2 represents a quadratic function translated left 4 units.