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, representing the basic shape before any transformations are applied.

Front

What is the equation of the absolute value parent function?

Back

f(x) = |x|

Front

How does shifting a graph to the right affect its equation?

Back

To shift a graph to the right by 'h' units, replace 'x' with 'x - h' in the function's equation.

Front

What is the effect of reflecting a graph over the x-axis?

Back

Reflecting a graph over the x-axis changes the sign of the output values, resulting in the equation being multiplied by -1.

Front

What is the equation of a quadratic parent function?

Back

f(x) = x²

Front

How do you shift a graph up by 'k' units?

Back

To shift a graph up by 'k' units, add 'k' to the function's output.

Front

What does the transformation 'left 2' mean in terms of the function's equation?

Back

To shift a graph left by 2 units, replace 'x' with 'x + 2' in the function's equation.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you identify a vertical shift in a function's equation?

Back

A vertical shift is identified by a constant added or subtracted from the function's output.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign in front of a quadratic function reflects the graph over the x-axis.