Transformations of Parent 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 transformation occurs when a function is reflected across the x-axis?

Back

The output values of the function are negated, resulting in a vertical flip of the graph.

Front

How does a horizontal shift to the right affect the equation of a function?

Back

A horizontal shift to the right by 'h' units is represented by replacing 'x' with 'x - h' in the function's equation.

Front

What is the effect of a vertical shift down on a function's graph?

Back

A vertical shift down by 'k' units is represented by subtracting 'k' from the function's output.

Front

What does a horizontal stretch by a factor of 'a' do to a function?

Back

A horizontal stretch by a factor of 'a' is represented by replacing 'x' with 'x/a' in the function's equation.

Front

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

Back

This represents a reflection of the absolute value function across the x-axis.

Front

How do you represent a vertical translation up by 3 units in a function?

Back

You add 3 to the function's output: f(x) + 3.

Front

What is the equation for a reflection over the y-axis?

Back

A reflection over the y-axis is represented by replacing 'x' with '-x' in the function's equation.

Front

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

Back

This indicates that the function is even, meaning it is symmetric about the y-axis.

Front

What is the effect of a vertical compression by a factor of 'b'?

Back

A vertical compression by a factor of 'b' is represented by multiplying the function's output by '1/b'.