Transformations of 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 is the parent function of a quadratic function?

Back

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

Front

What transformation does f(x) = -f(x) represent?

Back

Reflection over the x-axis.

Front

What transformation does f(x) = f(-x) represent?

Back

Reflection over the y-axis.

Front

What does a vertical shrink by a factor of ⅔ mean for the function f(x)?

Back

The output values of the function are multiplied by ⅔, making the graph closer to the x-axis.

Front

What does the transformation f(x - 7) indicate?

Back

A horizontal shift of the graph 7 units to the right.

Front

What does the transformation f(x) + 4 indicate?

Back

A vertical shift of the graph 4 units upward.

Front

What is the effect of a horizontal stretch by a factor of 2 on the function f(x)?

Back

The graph of the function is stretched away from the y-axis, making it wider.

Front

What does the transformation f(2x) indicate?

Back

A horizontal shrink by a factor of ½.

Front

What is the transformation represented by f(x) - 4?

Back

A vertical shift of the graph 4 units downward.