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 is the equation of the square root parent function?

Back

f(x) = √x

Front

What transformation occurs when a function is translated up 5 units?

Back

The function's output increases by 5 for every input, resulting in a vertical shift upwards.

Front

How does the graph of y = -|x| differ from y = |x|?

Back

The graph of y = -|x| is a reflection of y = |x| over the x-axis.

Front

What is the general form of a quadratic function?

Back

A quadratic function is generally expressed as f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does it mean to reflect a function over the y-axis?

Back

Reflecting a function over the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y).

Front

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

Back

A negative coefficient in front of a quadratic function causes the graph to open downwards.

Front

What is the equation of the cubic parent function?

Back

f(x) = x³

Front

How do you identify a quadratic function from its equation?

Back

A quadratic function can be identified by the presence of the x² term and its highest degree being 2.

Front

What transformation is represented by the equation y = (x - 3)²?

Back

This equation represents a horizontal translation of the parent function y = x² to the right by 3 units.