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 is the parent function of a quadratic function?

Back

The parent function of a quadratic function is f(x) = x².

Front

What is the parent function of an absolute value function?

Back

The parent function of an absolute value function is f(x) = |x|.

Front

What is the parent function of a linear function?

Back

The parent function of a linear function is f(x) = x.

Front

Describe the transformation represented by f(x - 4) - 2.

Back

This transformation represents a horizontal shift to the right by 4 units and a vertical shift down by 2 units.

Front

Describe the transformation represented by f(x + 4) - 2.

Back

This transformation represents a horizontal shift to the left by 4 units and a vertical shift down by 2 units.

Front

What effect does a positive value added to the function have on its graph?

Back

A positive value added to the function results in a vertical shift upward.

Front

What effect does a negative value subtracted from the input have on its graph?

Back

A negative value subtracted from the input results in a horizontal shift to the right.

Front

How does the graph of f(x) = x² compare to f(x) = (x - 3)² + 1?

Back

The graph of f(x) = (x - 3)² + 1 is a transformation of f(x) = x², shifted 3 units to the right and 1 unit up.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.